The band gap properties of one-dimensional photonic crystals with a defect layer of negative-refractive-index materials are studied. The defect mode width is larger than that of conventional one-dimensional photonic crystals with a defect layer of positive-refractive-index materials;The defect mode of the former is different from that of the latter. It will show a shift in the direction of high frequency,and has a bigger shifting velocity. Furthermore it is studied the effects on the transmission properties of the former photonic crystals caused by change in position of the defect layer with negative refractive index. Finally the optical enhancement of the former photonic crystals is also investigated.