Bounded traveling wave solutions of nonlinear telegraph equation were discussed by use of the theory and method of planar dynamical systems.The results indicate that the nonlinear telegraph equation has only two bounded traveling wave solutions.When the dissipation effect is strong,the bounded traveling wave solutions of nonlinear telegraph equation appear as kink solitary wave solutions; and when it is weak,they appear as damped oscillatory solutions.Based on the above discussion,a kink solitary wave solution corresponding to the strong dissipation effect,and approximate damped oscillatory solutions corresponding to the weak dissipation effect were obtained by using undetermined coefficients method.Furthermore,base on homogenization principle,the error estimates of approximate damped oscillatory solutions were given by establishing the integral equations reflecting the relations between exact solutions and approximate solutions.