Explicit traveling wave solutions of Fisher's equation with three simple zeros u t = u x x + u ( 1 − u ) ( u − a ) , a ∈ ( 0 , 1 ) , are obtained for the wave speeds C = ± 2 ( 1 2 − a ) suggested by pure analytic considerations. Two types of solutions are obtained: one type is of a permanent wave form whereas the other is not.