Abstract: The assumption of homoscedasticity is commonly concerned in regression analysis. In parametric and nonparametric regression models, the problem of testing of heteroscedasticity was discussed by Cook ＆ wesiberg （1983）, Eubank ＆ Thomas （1993） and Wei （1995）. In this paper, the testing of heteroscedasticity is researched for semiparametric regression model. The score test is obtained to test hypothesis of homoscedasticity and the asymptotic chi-squared property under the null hypothesis is proved. Simulations are done and we illustrate our test methods by using the mouthwash data （Speckman, P. （1988））.