No, no single book collects together all his stories, though they can be found on the net (except for a few slighter things and some of the revisions -- which were frequently entirely by HPL, but were ghost-written for someone else). However, Penguin in tpb has brought out really nice editions of all his work except for the revisions, and they are easily available. For everything, you'd need to go to Arkham House, and there's a 4-volume set that collects all of his fiction save for his prose-poems and some scattered non-weird work, which is collected in his
Miscellaneous Writings. But, if you wish to read his work, here's a site that you might want to look at:
the Complete works of H. P. Lovecraft
And, just in case you're interested in pursuing the ones mentioned above:
Penguin: The Call of Cthulhu and Other Weird Stories The Thing on the Doorstep and Other Weird Stories The Dreams in the Witch House and Other Weird Stories Arkham House: Dagon and Other Macabre Tales At the Mountains of Madness and Other Novels The Dunwich Horror and Others The Horror in the Museum and Other Revisions
These use the authoritative texts (earlier editions often had very corrupt texts), and are edited by S. T. Joshi, the leading Lovecraftian scholar.