Whale optimisation algorithm (WOA) is a new bio-inspired algorithm which mimics the hunting behaviour of humpback whale in nature. Standard WOA is easily trapped in local optima, provide slow convergence rate and lack of diversity, as the dimension of the search space expansion. In this paper, modified whale optimisation algorithm (MWOA) is proposed to improve the quality of standard WOA algorithm performance. Moreover, an adaptive optimisation algorithm based on modified whale optimisation algorithm and Laplace crossover (ALMWOA) is presented in this paper to increase the diversity of search space and enhance the capability to avoid local optimal solutions. The proposed MWOA and ALMWOA algorithms are tested on a set of 23 benchmark functions and the results are compared with standard WOA and other well-known meta-heuristic optimisation algorithms. Experimental results show that MWOA and ALMWOA can significantly outperform other optimisation algorithms in most of benchmark functions.