In this paper, we analyze the microstrip phase delay (PD) lines of different lengths are applied between the unit-cells (UCs) of leaky-wave antenna (LWA). The employment of PD lines can offer the phase compensations (PCs) for each UC, the simulation experiments observed that the PD lines can significantly improve the realized gain of LWA and reduce the operating bandwidth due to longer PD lines exciting the higher order modes of phase constant. Therefore, the scanning rates (SRs), i.e., scanning range divided by operating bandwidth (%), can remarkably increase. Besides, in order to maintain the beam scanning ability of LWA in travelling-wave direction (or longitudinal direction), the PD lines are placed and varied in the lateral direction. The phase constants in the lateral direction component are also proven to be able to excite higher order modes. Benefit from this, the multi-beam LWAs in the lateral direction can be obtained by the PD lines with optimal lengths, and patterns of multi-beam are fixed with the operating frequency changing.