Band structures of one-dimensional (1D) photonic crystals (PCs) containing dispersive left-handed metamaterials are studied theoretically. The results show that the structure possesses a type of photonic band gap originating from total internal reflection (TIR). In contrast to photonic band gaps corresponding to zero average refractive index and zero phase, the TIR gap exhibits sharp angular effect and has no polarization effect. It should also be noted that band structures of transverse electri