I first read George R.R. Martin's fiction in the late Seventies. I can't recall if the first of his books that I encountered was the short story collection A Song for Lya, or the novel Dying of the Light. Both are excellent, by the way, and both foreshadow the Martin mega-saga that has now become the TV series Game of Thrones.
What Martin did in his early, award-winning sf was emulate earlier authors, notably Robert Heinlein, Cordwainer Smith, and Larry Niven, by creating a detailed future history. In the universe he imagined the human race struck out for the stars, colonised strange and scary worlds, and encountered interesting and sometimes very powerful aliens. Most of his early stories, plus that one straight sf novel, were set in a galaxy some centuries after a catastrophic war with two rival alien empires fragmented the human race into various regional powers. This Balkanised sector of the galaxy, the Manrealm, was a backdrop for some well-written, often lyrical, and sometimes violently action-packed tales.
Unfortunately, like so many before him, Martin didn't make a living from writing very good science fiction. So, to the slight bafflement of admirers like me, after collaborating with Lisa Tuttle on a rather good 'low-tech' sci-fi novel, Windhaven, he tried his hand at writing novels in the rather different (albeit related) horror genre. The results, Fevre Dream and The Armageddon Rag, are both rather good.
Fevre Dream is the story of the eponymous Mississippi riverboat that becomes a floating vampire lair. Interestingly Martin, perhaps because of his sf background, gives his vampires no supernatural qualities - they are predatory human-like sub-species, possessed of great strength and hypnotic powers, but not actually undead. I recall enjoying this one a lot at the time, not least because of Martin's smoothly efficient inclusion of a lot of research material on the pre-Civil War US.
The second novel is a foray into Stephen King territory, to some extent, with its central premise - a revived Sixties rock group that is somehow primed to bring about apocalyptic events. I can see why people didn't like The Armageddon Rag - it's not feel-good fiction, though it's well-written and full of interesting (and sometimes amusing) characters.
Martin also produced some very good short fiction that does qualify as supernatural. The story 'Portraits of his Children', for instance, is about a self-absorbed writer who cares more about his characters than his own family. He gets a very well-described comeuppance in a tale that explores the blatant egotism that undoubtedly drives many a bestselling author. 'The Monkey Treatment' is a grimly comic tale of an obese man who seeks an unorthodox weight loss method. Another early story, 'Sandkings', about alien social insects that are unwisely kept as pets, was adapted as a rather disappointing episode of the revived Outer Limits.
Most Martin's short fiction has been collected in Dreamsongs, a two-volume set. I can recommend it to anyone who likes well-crafted stories that are, by and large, tightly plotted, strong on character, and full of interesting ideas.