Cuckoo Search (CS) is a Meta-heuristic method, which exhibits several advantages such as easier to application and fewer tuning parameters. However, it has proven to very easily fall into local optimal solutions and has a slow rate of convergence. Therefore, we propose Modified cuckoo search algorithm with variational parameter and logistic map (VLCS) to ameliorate these defects. To balance the exploitation and exploration of the VLCS algorithm, we not only use the coefficient function to change step size $\alpha$ and probability of detection $p_a$ at next generation, but also use logistic map of each dimension to initialize host nest location and update the location of host nest beyond the boundary. With fifteen benchmark functions, the simulations demonstrate that the VLCS algorithm can over come the disadvantages of the CS algorithm.In addition, the VLCS algorithm is good at dealing with high dimension problems and low dimension problems.