Recently, several vector hysteresis models such as vector Preisach, vector Jiles-Atherton and dynamic E&S model have been proposed to describe vector magnetic properties of electrical steel sheets. However, it is still difficult to find an adequate vector hysteresis model in finite element application for both the Non-oriented and Grain-oriented electrical steel sheets under alternating and rotating field conditions. In this paper, an improved E&S vector hysteresis model is suggested to describe the vector magnetic properties of both Non-oriented and Grain-oriented electrical steel sheets under various magnetic field conditions including alternating and rotating magnetic field conditions. The validity of the proposed model is tested through comparisons with the experimental results under various magnetic field conditions.