A random walk dan be used to model various types of discrete random processes. It may be of interest at some point to find the peak of this function. A direct method of doing so involves evaluating the function at every point and recording the highest value. However, it may be desirable to find the peak without having, to evaluate the function at every point. A search technique was developed to find the peak of a random walk with a minimal number of function evaluations using probabilistic means to guess at where the peak will most likely occur given the parameters of a specific function. A computer program was written to implement the search strategy and a series-of random walk functions of varying lengths were generated to test its performance. Data was compiled and the results show that the search is capable of finding the peak with a significant reduction in the number of function evaluations needed for a point by point search, especially for functions of greater walk length.