In order to solve the problem of low precision of monarch butterfly optimization(MBO)causing by diversity degradation and being easy to fall into local optimum, a self-adaptive monarch butterfly optimization based on nonlinear cloud-transfer(NCSMBO) is proposed. The evolution mechanism of the MBO is deeply explored which indicates the nature of the MBO is grid search. Nonlinear cloud-transfer operation to parent monarchs is executed utilizing a forward normal-cloud generator in both migration operators and adjusting operators, which can increase candidate solutions and improve the ability of local exploitation. Meanwhile, a greedy strategy is introduced in offspring from a cloud-transfer to enhance the feasibility. A self-adaptive adjustment rate in the form of double-circle-tangent is given to control mutation based on occurrence probability. Seven optimization algorithms including the NCSMBO are overall evaluated on the 12 benchmark functions with different features, and two types of mathematical planning problems are solved and verified. All of the simulation results show that the proposed algorithm has better convergence accuracy and stability.