Abstract: We consider ITô-VOLTERRA SDE: X_t=X_0+\int_0^t a\left(t, s, x_0\right) d w_0+\int_0^t b\left(t, s, x_s\right) d s, Where EX⁴＜∞, 0≤t≤T, T＞0, W is a Standard Brown Motion. So far, many authors （for exemple （2）, （3）, （6）） have only proved the existence of the strong solution. Different from the other authors, this paper obtains a sufficient condition of the existence of the weak solution, where a, b \frac\partial a\partial t and \frac\partial b\partial t are bounded continuous functions on 0,T²×R¹.