The paper is aimed at modeling the enhanced Kerr nonlinearity in a five-level double-ladder-type atomic system based on electromagnetically induced transparency (EIT) by using the semi-classical density matrix method. We present an analytical model to explain the origin of Kerr nonlinearity enhancement. The scheme also results in a several orders of magnitude increase in the Kerr nonlinearity in comparison with the well-known four- and three-level atomic systems. In addition to the steady-state case, the time-dependent Kerr nonlinearity and the switching feature of EIT-based colossal Kerr nonlinearity is investigated for the proposed system.