The focus of this paper is on small low-cost turbojet engines equipped with a gear-type fuel pump rather than a more traditional fuel metering unit. The incorporation of such type of fuel flow actuation devices introduce additional nonlinearities into the system and therefore make traditional modeling and system identification methods difficult to apply. In this paper, we propose a nonlinear fast engine model structure that can be used for various applications, including identification, modeling and simulation, and controller design of such sub-class turbojet engines. A high-fidelity turbojet engine model including its nonlinear gear-type fuel pump is developed, which is later used to generate the fast engine model. The parameters of the fast engine model are estimated using regression analysis. The identification procedure is also applied to real engine test data to verify the proposed approach.