This paper studies the hypothesis problem of partially linear single index model with responses missing at random.The nonlinear relationship between the predictors and response variable is tested.To test the nonparametric part of this model,the missing responses are imputed based on the imputation estimators of the parameters and nonparametric function.The generalized likelihood ratio statistic is constructed based on the imputation estimators,and the asymptotic property of the statistic is also proved.