A relativistic Cherenkov source with slow wave system consisting of modified photonic band-gap cells is proposed and investigated. The high frequency structure simulator and three-dimensional particle-in-cell simulation code are used to study the dispersion characteristic of TM01-like mode and the interaction between electromagnetic wave and electron beam. The results show that, in the slow wave system with modified photonic band-gap cells, the TM01-like mode has much better azimuthal symmetry, the non-axisymmetry mode can be efficiently suppressed and the operation efficiency can be enhanced greatly.