In this paper, a new kind of admittance inverter and design of a switchable microstrip bandpass filter using composite right/left-handed (CRLH) cells has been presented. The proposed filter has two states (or passbands). One of the two passbands, is accessible at each time by on/off state of three PIN diodes. This filter is a three-pole, coupled resonator filter, composed of short-circuited shunt resonators. These resonators are coupled using admittance inverters. With regard to the characteristics of the equivalent circuit of CRLH cells, a new structure of admittance inverter (J-inverter) has been introduced. This novel J-inverter has PI-section equivalent circuit and it consists of both inductive and capacitive elements. In our work, the proposed J-inverter was mathematically studied and the switchable filter was simulated and implemented. The results of simulations for the first and second state of the filter, which are frequency bands of (Δ1 = 0.11 and f1 = 1.26 GHz) and (Δ2 = 0.12 and f2 = 1.5 GHz), are verified by measurements.