With rapid development of advanced manufacturing technologies and high demands for innovative lightweight constructions to mitigate the environmental and economic impacts, design optimization has attracted increasing attention in many engineering subjects, such as civil, structural, aerospace, automotive and energy engineering. For nonconvex nonlinear constrained optimization problems with continuous variables, evaluations of the fitness and constraint functions by means of finite element simulations can be extremely expensive. To address this problem by algorithms with sufficient accuracy as well as less computational cost, an extended multipoint approximation method (EMAM) and an adaptive weighting-coefficient strategy are proposed to efficiently seek the optimum by the integration of metamodels with sequential quadratic programming (SQP). The developed EMAM stems from the principle of the polynomial approximation and assimilates the advantages of Taylor’s expansion for improving the sub-optimal continuous solution. Results demonstrate the superiority of the proposed EMAM over other evolutionary algorithms (e.g. particle swarm optimization technique, firefly algorithm, genetic algorithm, metaheuristic methods and other metamodeling techniques) in terms of the computational efficiency and accuracy by four well-established engineering problems. The developed EMAM reduces the number of simulations during the design phase and provides wealth of information for designers to effectively tailor the parameters for optimal solutions with computational efficiency in the simulation–based engineering optimization problems.