The research on surrogate-assisted evolutionary algorithms has attracted increasing attention for time or resource consuming optimization problems over the past decades. However, most existing surrogate-assisted evolutionary algorithms still require thousands of expensive function evaluations to obtain acceptable solutions and are only applied to low-dimensional problems. Therefore, a surrogate-assisted optimization, called SMIC-SLPSO (Similarity-based multipoint infill criterion for surrogate-assisted social learning particle swarm optimization), is proposed for high dimensional problems with less computation. In the proposed algorithm, using Gaussian process as the surrogate model and considering SLPSO algorithm as an optimizer, a similarity-based multipoint infill criterion (SMIC) is proposed for searching the solutions to re-evaluation by using the original expensive problems. Simulation of experiments comparing the proposed algorithm with a few state-of-the-art surrogate-assisted evolutionary algorithms on benchmark functions from 50 to 100 dimension is carried out. The results proposed algorithm is able to achieve better or competitive solutions with a limited budget of exact evaluations, especially on higher dimensional problems.