The growth behavious of interfaces in order parametes-conservation system with spatial correlation are analysed by using renormalization-group method. The scaling exponentχ and dynamic exponent z are obtained as functions of spatial dimension d and roughening exponent ρ. The result shows that the conservation condition makes the fluctuation Propagation decay, and spatial correlations make the interface roughen. The results are also compared with that of E. Medina et al. and T. Sun et al.