A periodic microstrip leaky wave antenna (MLWA) constructed of non-uniform aspect ratios microstrip patch periods is presented in this communication. Effective equations and simulations for the relevant antennas are used to obtain the propagation constants of the proposed antenna and design it. However, due to the presence of an open stop-band (OSB) in the broadside direction, double-side parallel-strip lines are then introduced in the antenna design. Truncating and interlacing the unit cells are developed to make them become impedance matched structures with the elimination of the OSB and the improvement of the radiation patterns. As a result, a new antenna configuration is created, and a prototype of the antenna is fabricated and measured. Continuous main beam scanning is observed from back-firing to end-firing with the operating frequency band of 4.8-18 GHz. Excellent agreements between the predicted and measured results are obtained. The measured peak gain of the prototype is 14 dBi, and the gain exceeds 6 dBi over the frequency band.