In this paper, a novel efficient learning algorithm towards self-generating fuzzy neural network (SGFNN) is proposed based on ellipsoidal basis function (EBF) and is functionally equivalent to a Takagi-Sugeno-Kang (TSK) fuzzy system. The proposed algorithm is simple and efficient and is able to generate a fuzzy neural network with high accuracy and compact structure. The structure learning algorithm of the proposed SGFNN combines criteria of fuzzy-rule generation with a pruning technology. The Kalman filter (KF) algorithm is used to adjust the consequent parameters of the SGFNN. The SGFNN is employed in a wide range of applications ranging from function approximation and nonlinear system identification to chaotic time-series prediction problem and real-world fuel consumption prediction problem. Simulation results and comparative studies with other algorithms demonstrate that a more compact architecture with high performance can be obtained by the proposed algorithm. In particular, this paper presents an adaptive modeling and control scheme for drug delivery system based on the proposed SGFNN. Simulation study demonstrates the ability of the proposed approach for estimating the drug's effect and regulating blood pressure at a prescribed level.