We extend a class of a one-dimensional smooth map.We make sure that for each desired interval of the parameter the maps Lyapunov exponent is positive.Then we propose a novel parameter perturbation method based on the good property of the extended one-dimensional smooth map.We perturb the parameter r in each iteration by the real number x2 generated by the iteration.The auto-correlation function and NIST statistical test suite are taken to illustrate the methods randomness finally.We provide an application of this method in image encryption.Experiments show that the pseudo-random sequences are suitable for this application.