We consider a semiparametric varying-coefficient proportional hazards model with current status data. This model enables one to assess possibly linear and nonlinear effect of certain covariates on the hazard rate. B-splines are applied to approximate both the unknown baseline hazard function and the varying-coefficient functions. To improve the performance of the model, ridge penalty is added to the log-likelihood to penalize the roughness of the cumulative hazard function. Efficient sieve maximum likelihood estimation method is used for estimation. Simulation studies with the weighted bootstrap method are conducted to examine the finite-sample properties of the proposed estimators. We also present an analysis of renal function recovery data for illustration.