It is quite challenging to attain an accurate reliability estimation on complex structures with low computational burden. Therefore, an active learning method combining the response surface model with the Gaussian process (GP) of residual fitting and reliability-based sequential sampling design is proposed for structural reliability analysis. This method first utilizes a random quadrilateral grid to perturb the uniform design sampling and generates a small set of initial DoE to establish a high-precision initial response surface model (RSM) efficiently. Then, a GP model for residual prediction is constructed by using the residuals of the initial RSM, which allows the response surface function to be closer to the limit state function. A reliability-based EI learning function, which inherits the property of the EI function and considers the probability of feasibility of the samples, is developed for the selection of the most feasible points to update the surrogate model. Ultimately, four numerical examples are used to validate the accuracy and efficiency of the proposed method.