We present an analytical model for cross-Kerr nonlinear coefficient in a four-level N-type atomic medium under Doppler broadening.The model is applied to 87Rb atoms to analyze the dependence of the cross-Kerr nonlinear coefficient on the external light field and the temperature of atomic vapor.The analysis shows that in the absence of electromagnetically induced transparency (EIT) the cross-Kerr nonlinear coefficient is zero,but it is significantly enhanced when the EIT is established.It means that the cross-Kerr effect can be turned on/off when the external light field is on or off.Simultaneously,the amplitude and the sign of the cross-Kerr nonlinear coefficient are easily changed according to the intensity and frequency of the external light field.The amplitude of the cross-Kerr nonlinear coefficient remarkably decreases when the temperature of atomic medium increases.The analytical model can be convenient to fit experimental observations and applied to photonic devices.