Abstract: This paper discusses a randomized non-autonomous logistic equation , where is a 1-dimensional standard Brownian motion. In [D.Q. Jiang, N.Z. Shi, A note on non-autonomous logistic equation with random perturbation, J. Math. Anal. Appl. 303 (2005) 164–172], the authors show that has a unique positive T-periodic solution provided , and are continuous T-periodic functions, , and . We show that this equation is stochastically permanent and the solution is globally attractive provided , and are continuous T-periodic functions, , and . By the way, the similar results of a generalized non-autonomous logistic equation with random perturbation are yielded. [Copyright &y& Elsevier]