a new kind of surface -conduction electron -emitter (sce) with a triangular dielectric layer under the conductive film is proposed. the influences of the vertex angle (theta) of the triangular dielectric layer and the anode voltage (u-a) on the electron emission efficiency and the focusing capability have been investigated with the finite integration technique (fit). the numerical simulation results show that sce with a small vertex angle guarantees higher electron emission efficiency even with a low anode voltage. but the focusing capability of the electron emitter will get worse when the theta or u-a becomes too small. take both the electron emission efficiency and focusing capability into consideration, the structure with a vertex angle (theta) between 60 degrees-100 degrees and the anode voltage of 1500 v is suggested.