The Cox proportional hazards model for censored failure time data with possible time-varying covariates assumes that the relationship between the baseline hazard function and the exponential regression function of covariates is multiplicative. The violation of this assumption may have adverse effects on the statistical inferences. The existing graphical as well as numerical procedures for checking this assumption are either subjective or confined to special situations. In this paper, we develop a global goodness-of-fit test for the general Cox model. The test is derived from Cox's partial likelihood. The proposed statistic has asymptotically chi-square distribution with suitable degrees of freedom. An example on a prostate cancer problem with tumour size and weight as covariates is considered.