26D10, 26D20, 60H05, 60H35

In this paper, we show a Gronwall type inequality for Ito integrals (Theorems 1.1 and 1.2) and give some applications. Our inequality gives a simple proof of the existence theorem for stochastic differential equation (Example 2.1) and also, the error estimate of Euler-Maruyama scheme follows immediately from our result (Example 2.2}).;