For detecting wavefronts from the system with long optical path or multi-component lens with one by one aligning, the phase-shifting lateral shearing interferometry of convergent beam with the convergent beam as light source for interferometry is proposed, which is based on Michelson interferometer. The mathematical expression of the laterally shifted wavefront of convergent beam is established and compared with that of general lateral shearing interferometers. The shearing and wavefronts displacement are analyzed, and the phase-shifting interferometry is adopted to obtain the sheared wavefronts. The results show that the lateral shearing phase-shifting interfermetry of convergent beam can measure the real-time wavefronts of convergent beam with repetitions of peak-valley (PV) value and root-mean-square (RMS) of 0.022λ and 0.014λ respectively. The experimental results are compared with that by Zygo interferometer, which proves the validity of the proposed technique.