Focusing on the nonlinear transmission equation in the gradedindex waveguides, the nonlinear dynamic behaviors of the rogue wave in a planar amplifier were studied. The similarity transformation and direct hypothesis were used to construct the first order rogue wave solution with arbitrary function. On the basis of the solution, different rogue waves were obtained by the numerical simulation in view of different types of free function. It is significant to describe the physical phenomena in the optical fibers.