Lead halide perovskite (APbX3) nanocrystals exhibit photoluminescence (PL) with both wide wavelength tunability and high quantum efficiency. While the Pb-X6 octahedra mainly determines the near-band-edge optical properties and the A-site cation affects the structural stability, the role of the A-site cation in determining the optical properties is still unclear. Here, we report the PL properties of three types of lead bromide perovskite APbBr3 nanocrystals with different cations [A = HC(NH2)2+, CH3NH3+, and Cs+], as revealed by single-dot spectroscopy, and discuss the influence of the A-site cation on the PL spectrum. The nanocrystal size dependences of the PL energy and lifetime show no large variation with the species of the A-site cation. We find that the size of the A-site cation determines the coupling strength between electrons and longitudinal-optical phonons in the nanocrystal and thus affects the PL spectral shape, especially the low-energy tail.