No I don't think his blood status is mentioned in the books but people believe he is Halfblood with a Pureblood father and muggle born witch mother because of Skeeters articles and Muriel saying his mother was ashamed to be muggleborn. All this is speculation though.
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Is it mentioned wheather, Kendra Dumbledore (Albus' mother),is muggleborn?
Anyway, if Kendra was muggleborn then Albus Dumbledore would have been halfblood and if his mother had been a pure-blood then he would have been a pure-blood because his father was also a pure-blood.
i am not sure if hes pure blood but i don't think so because i think his mother was muggle born and his father was pure blood so i guess it means hes a half blood