The study of the Diophantine equation x2-Dy4=N ( D and N are the given integers, D > 0 and D is non-square ) has caused some authors’ interests, such as Cohn, Tzanakis, LI Jin-xiang ， LIN LI-juan. Cohn has proven some conclusions. For example: N(5, 44)=1 ， (x, y)=(7 ， 1); N(5 ， 11)=2, (x, y)=(4,1) ， (56,5); N(5 ， -44)=3 ， (x, y)=(6 ， 2) ， (19 ， 3) ， (181 ， 9). Tzanakis has proven some conclusions while y≡0 (mod8). For example: N(2, 17)=0, N(2, 41)=0, N( 8 ， 17)=0, N(2, 97)=0. LI Jin-xiang hasproven one conclusion: N(3, 46)=2, (x, y)=(7,1) ， (17, 3). LIN Li-juan has also proven one conclusion: N(3, 22)=2 ， (x, y)=(5, 1) ， (85, 7). But this Diophantine equation x2-3y4=166 still has not been solved until now. In this paper the author has proved that the Diophantine equation x2-3y4=166 has only positive integral solutions(x, y)=(13 ， 1) ， (293 ， 13) with the primary methods of recursive sequence ， quadratic remainder and congruence.