In this paper, the kinetics and morphology of viscoelastic microphase separation of diblock copolymers are investigated in detail. It is found that for a symmetric system (f=0.5), taking into account the bulk modulus differences between the two blocks, the classical randomly oriented lamellar morphology is not observed. Instead, we find that droplets of the lower bulk modulus soft block disperse in a matrix of higher bulk modulus hard block. In the case of off-critical system (f=0.4), since an inherent composition asymmetry exists between the two blocks, the viscoelastic microphase separated morphology is also different from that normally observed, whether there is an apparent difference in the bulk moduli between two blocks. However, when a bulk modulus difference exists between the two blocks, the morphology is further altered. Addition of random thermal noise to both the critical (f=0.5=and the off-critical system (f=0.4=weakens the suppression of concentration fluctuations, but no fundamental structural transformation is caused by the noise. Since the abnormal morphology is observed on slow approach to the equilibrium state, we conclude that the viscoelastic effect may be largely responsible for the observed deviations between the experimentally measured and the mean-field theoretically calculated phase diagrams.