For any positive integer , the Smarandache double factorial is defined as the smallest integer such that , where m!!=1·3·5…m, 2n2·4·6…m, 2n . The paper conducts the study of the mean value of the Smarandache Double Factorial function by the elementary and analytic methods, obtains a sharper asymptotic formula for the Smarandache Double Factorial function , and thus solves the problem proposed by Felice Russo in reference \[4\] .