New phases of Si3N4 that may be stable at higher pressure than spinel have been searched using a first-principles plane-wave pseudopotential method. The CaTi2O4-type phase is found to be the prime candidate for the post-spinel phase among six phases selected on the analogy to high-pressure oxides. The phase transformation from the spinel is predicted to occur at 210 GPa. All silicon atoms of the new phase are coordinated by six anions, similar to the case of the high-pressure forms of SiO2 and SiC. Because of its high energy at zero pressure, this new phase may be difficult to quench. The bandgap increases with an increase of pressure when compared in the same polymorph. However, the bandgap and the net charge decrease In the order of beta, spinel, and CaTi2O4-type phases at zero pressure. The theoretical bulk modulus of the CaTi2O4-type phase is comparable with that of spinel.