Visual servoing (VS) based on the Kalman filter (KF) algorithm, as in the case of KF-based image-based visual servoing (IBVS) systems, suffers from three problems in uncalibrated environments: the perturbation noises of the robot system, error of noise statistics, and slow convergence. To solve these three problems, we use an IBVS based on KF, African vultures optimization algorithm enhanced extreme learning machine (AVOA-ELM), and fuzzy logic (FL) in this paper. Firstly, KF online estimation of the Jacobian matrix. We propose an AVOA-ELM error compensation model to compensate for the sub-optimal estimation of the KF to solve the problems of disturbance noises and noise statistics error. Next, an FL controller is designed for gain adaptation. This approach addresses the problem of the slow convergence of the IBVS system with the KF. Then, we propose a visual servoing scheme combining FL and KF-AVOA-ELM (FL-KF-AVOA-ELM). Finally, we verify the algorithm on the 6-DOF robotic manipulator PUMA 560. Compared with the existing methods, our algorithm can solve the three problems mentioned above without camera parameters, robot kinematics model, and target depth information. We also compared the proposed method with other KF-based IBVS methods under different disturbance noise environments. And the proposed method achieves the best results under the three evaluation metrics.