If $X_1,\dots,X_n$ are independent geometric random variables with parameters $p_1,\dots,p_n$ respectivelly, we prove that the function $F(p_1,\dots,p_n;t) = P(X_1+\dots+X_n\leqt)$ is Schur-concave in $(p_1,\dots,p_n)$ for every real $t$. We also give a new proof for a theorem due to P. Diaconis on Schur-convexity of distribution fuction of linear combination of two exponential random variables.