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In this paper, we develop a simple test procedure for comparing the cause-specific hazard rates of a competing risks model based on a right censored (competing risks) data. Asymptotic distributions of the test statistic under both the null and alternative hypotheses are shown to be normal by expressing the statistic in terms of counting processes and using martingale central limit theory. These results enable us to assess the power of the test analytically rather than through simulations. The power comparison of the test with some existing tests shows that the proposed test performs better in the presence of censoring. An application of the test for comparing the risks of two types of cancer mortality (thymic lymphoma and reticulum cell carcinoma) in a strain of laboratory mice is illustrated.