The surrogate-assisted evolutionary algorithm (SAEA) is an effective way to solve expensive problems. This study proposed a diversity-based surrogate-assisted evolutionary algorithm (DSAEA) to solve the expensive multi-objective optimization problem. DSAEA approximates each objective with the Kriging model to replace the original objective function evaluation, accelerating the optimization process of the evolutionary algorithm. It decomposes the problem into several subproblems with the reference vectors. The correlation between the solution and the reference vector is established according to the angle between them. Then the minimum correlative solution set is computed. Based on it, the candidate producing operator and the selection operator tend to preserve the solutions of diversity. In addition, as the training set, Archive A is updated after each iteration, deleting the little value samples according to diversity to reduce the modeling time. In the experiment section, large scale 2- and 3-objective comparative experiments for DSAEA and several current popular SAEAs were done. Each algorithm on different test problems ran 30 times independently, and the inverted generational distance (IGD), hypervolume (HV), and running time were calculated and collected. At last, rank sum test was used to analyze the experimental results. The results show that DSAEA performs better on the most experimental test problems, therefore, it is effective and feasible.