A multi-level atomic system is a controllable optical medium for obtaining Kerr nonlinearity. This paper aims at theoretical research on Kerr nonlinearity in five-level double-ladder ⁸⁷Rb atomic system.Using the semi-classical density matrix equations along with an iterative perturbation technique,analytical expressions of the linear and nonlinear susceptibilities are derived for stationary as well as for moving atoms.Research has shown that,this five- level atomic medium exhibits multiple electromagnetically induced transparency (EIT) at four fields with quantum coherent,at the same time,the Kerr nonlinearity is always inversely correlated with the absorption spectrum,and a pair of positive-negative peaks of Kerr nonlinearity coefficients appear in each EIT region.It also elucidated the Doppler effect broadens the absorption spectrum while narrowing the dispersion slope.This analytical model can easily fit experimental data and be applied to photonic devices.