This letter presents a vertically polarized (VP) endfire leaky-wave antenna (LWA) by periodically loading shunt inductive cavity at two sides of the double-sided parallel strip line. Different from the most of nonuniform LWA with matched phase at single frequency, the proposed one can realize the matched phase constants in the operating band with adjusted attenuation constant values along antenna for certain distribution. The structural influences are investigated to explore the proper loading configuration to meet the requirements for the propagation constants. It is found that the widths of the inductive loading cavity and its connecting line can be employed to control the attenuation constants obviously with weak effects on phase values and slopes in the operation band. In this way, a nonuniform prototype antenna with Taylor distribution is designed to prove its ability of flexibly controlling propagation constants in the operation range. The simulated results agree well with the measured ones, which confirms the merits of proposed loading strategy in realizing some specific radiation performances.