Cox model is important and used in many fields.This paper extends Cox model to semiparaemtric varying-coefficient regression model and proposes estimation of parameters and varying-coefficients in semiparametric varying-coefficient regression.The proposed model, includes intercept function that can explain effect of some factor., is an extension of existed models in literature.However statistic inference of this function is very difficult because of loss of its estimable directly in partial likelihood function.A profile estimation on the parameters can be obtained by maximizing a profile partial-likelihood which enables the estimators of the parametric component to be-consistent.It is shown that the nonparamctric component can be estimate as well.Asymptotic normality is also obtained for the profile estimates of both the parametric and nonparametric components.Simulations are conducted to demonstrate the performance of the proposed method.