In this article, we propose using the L2 divergence to test the Exponentiality for random censored data. Then we compare the ability of the proposed test to detect the Exponential distribution by Monte Carlo simulation with other competing tests, including the Kolmogorov‐Smirnov, Anderson‐darling and Cramer von‐Mises tests, which are based on the empirical distribution function and the information criteria tests. The results of simulation studies show that the proposed test generally performs better than its competitor tests.