In order to study the dynamic scaling behavior of the space-fractional stochastic growth equation with correlated noise, we simulate numerically the space-fractional Edwards-Wilkinson (SFEW) equation driven by correlated noise in (1+1)-dimensional case based on the Riesz-and the Grmwald-Letnikov-type fractional derivatives. The scaling exponents including growth exponent, roughness exponent and dynamic exponent with different noise correlation factors and fractional orders are obtained, which are consistent with the corresponding scaling analysis. Our results show that the noise correlation factors and fractional orders affect the dynamic scaling behavior of the SFEW equation, which displays a continuous changing universality class.