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We consider the cosmetic surgery problem for two-bridge knots in the3-sphere. It is seen that all the two-bridge knots at most 9 crossings otherthan $9_{27} = S(49,19)=C[2,2,-2,2,2,-2]$ admits no purely cosmetic surgerypairs. Then we show that any two-bridge knot of the Conway form$[2x,2,-2x,2x,2,-2x]$ with $x \ge 1$ admits no cosmetic surgery pairs yieldinghomology 3-spheres, where $9_{27}$ appears for $x=1$. Our advantage to provethis is using the $SL(2,\mathbb{C})$ Casson invariant.

Cosmetic surgery and the $SL(2,\mathbb{C})$ Casson invariant for two-bridge knots