We give a criterion for the log-convexity (resp.the strong q-log-convexity) in terms of certain infinite triangular array of nonnegative numbers (resp.of polynomials in q with nonnegative coefficients).Our result allows a unified treatment of the log-convexity of many classical combinatorial numbers, as well as that of the q-log-convexity of some classical polynomials.In particular, we obtain simple proofs of the q-log-convexity of Narayana polynomials.