This paper presents minimum mean square error (MMSE) estimators for mean life and failure rate of Exponential distribution model based on failure censored step-stress accelerated life-testing (SSALT) data. The MMSE estimators are drived by revising the corresponding unbiased estimators in terms of mean square error (MSE). Two theorems prove mathematically the fact that MSE of the resulting MMSE estimators are smaller than that of the corresponding unbiased estimators. The results show that the MMSE estimators are more efficient than the unbiased estimators and maximum likelihood estimators (MLEs) in small and moderate sample size.