He is a non-cognitivist and even emotivist, as is clear from passages like:
To have the sense of virtue, is nothing but to feel a satisfaction of a particular kind from the contemplation of a character. The very feeling constitutes our praise or admiration.
We go no farther; nor do we inquire into the cause of the satisfaction. We do not infer a character to be virtuous, because it pleases: But in feeling that it pleases after such a particular manner, we in effect feel that it is virtuous.
The case is the same as in our judgments concerning all kinds of beauty, and tastes, and sensations. Our approbation is implied in the immediate pleasure they convey to us. (3.1.2)
However, later on in the same chapter he proposes a powerful objection to his own theory.
Remember that the proper metaethics is (1) cognitivist, (2) actuated by 1st-order desires, (3) externalist. But the proper conception of physical goods is (1') non-cognitivist -- a thing's goodness (for me) is expressed in my enjoyment of it, (2') also driven by 1st-order desires, and (3') internalist, wherein the connection between judgment and motivation is that the motivation to pursue a pleasure causes the judgment "it is good" to be true.
If, following Hume, we mistakenly deem metaethics to be non-cognitivist + internalist, then how do we tell apart metaphysical goods (say, the nobility of charity or the wickedness of murder) from physical goods (say, the pleasure of eating ice-cream or the awfulness of the screech of monkeys)? "If virtue and vice be determined by pleasure and pain, these qualities must, in every case, arise from the sensations; and consequently any object, whether animate or inanimate, rational or irrational, might become morally good or evil, provided it can excite a satisfaction or uneasiness." Hume's first reply is that the pleasures and pains associated with virtue and vice are "peculiar" and presumably uniquely different from any pleasure produced by a merely material object.
Hume will then say than a wine, music, and man are good because they cause pleasure but for different qualities; thus, wine is good for its flavor; music, for its harmony; and man, for his virtue. But there is a problem. Wine and music are my bitches. They exist solely for my pleasure and are thrown away with contempt and indifference or even hatred when I find them tiresome. On the other hand, a girl is not a mere device that assists my masturbation. A human being is not a consumer good. At the very least, then, we must acknowledge that good wine is good physically, and a good man is good metaphysically. Hume is indicating that the goodness of both is, despite this obvious distinction, fully derivative from the pleasure they cause to us. This is plausible for wine. But wouldn't the man still be good, such as charitable or brave or loyal to his friends or cause even if I never knew of him? Isn't it in fact a test of my moral goodness to admire him for these virtues? I am not at this moment distinguishing between subjective vs. objective goodness, though this is a worthy subject in its own right; merely between judgment that is obtained from sentiment in physical good vs. sentiment that is obtained from judgment in metaphysical good. For the former, I love X, and then and because of it, X becomes good. For the latter, Y is good, and then I had better love Y (or else).
Hume's second argument is problematic, as well. He writes that the peculiarity of the feelings that virtue excites in us lies in their nature of pride / humility and love / hatred. I have written that the former are aspects of self-love. Regarding the latter, hatred for a fellow man is unnatural, as in, never justified, thereby being below human nature; at the same time loving another human being is impossible without divine grace which is above nature. (Thus, falling in love is due to the bestowal of grace; and mothers, too, I think, are given grace to love their children.) Since his book is a treatise on human nature as opposed to beastliness or deiformity, Hume is not allowed to invoke hatred or love in his arguments.