In multiobjective evolutionary algorithms, how to select the optimal solutions from the offspring candidate set significantly affects the optimization process. At present, the selection of the optimal solutions is largely based on the real objective values or surrogate model to estimate objective values. However, these selections are usually very time-consuming or of poor accuracy problems, especially for some real complex optimization problems. Recently, some researchers began to employ supervised classification to assist offspring selection, but these works are difficult to prepare the exact positive and negative samples or of time-consuming parameter adjustment problems. In order to solve these disadvantages, a novel hybrid individual selection mechanism is proposed through integrating classification and surrogate to select the optimal solutions from the offspring candidate set. Concretely, in each generation, the selection mechanism employs a classifier to select good solutions firstly; then, it designs a cheap surrogate model to estimate objective values of each good solution; finally, it sorts these good solutions according to objective values and selects the optimal solution as the offspring solution. Based on the typical multiobjective evolutionary algorithm MOEA/D, the hybrid individual selection mechanism is employed to design a new algorithm framework MOEA/D-CS. Compared with the current popular multiobjective evolutionary algorithms based on decomposition, experimental results show that the proposed algorithm obtains the best performance.