A multifidelity surrogate (MFS) model is a data fusion method for the enhanced prediction of less intensively sampled primary variables of interest (i.e., high-fidelity (HF) samples) with the assistance of intensively sampled auxiliary variables (i.e., low-fidelity (LF) samples). In this article, an MFS model based on the gradient-enhanced radial basis function, termed gradient-enhanced multifidelity surrogate based on the radial basis function (GEMFS-RBF), is proposed to establish a mapping relationship between HF and LF samples. To identify the scaling factor and the undetermined coefficients in GEMFS-RBF, an expanded correlation matrix is constructed by considering the correlations between the acquired samples, the correlations between the gradients, and the correlations between the samples and their corresponding gradients. To evaluate the prediction accuracy of the GEMFS-RBF model, it is compared with the co-Kriging model, multifidelity surrogate based on the radial basis function (MFS-RBF) model, and two single-fidelity surrogate models. The influences of key factors (i.e., the correlations between the HF and LF functions, the subordinations between the sample sets) and the effect of the cost ratio on the performance of GEMFS-RBF are also investigated. It is observed that GEMFS-RBF presents a more acceptable accuracy rate and is less sensitive to the aforementioned factors than the other benchmark models in most cases in this article, which illustrates the practicability and robustness of the proposed GEMFS-RBF model.