The forward full-wave modeling of ground-penetrating radar (GPR) facilitates the understanding and interpretation of GPR data. Traditional forward solvers require excessive computational resources, especially when their repetitive executions are needed in signal processing and/or machine learning algorithms for GPR data inversion. To alleviate the computational burden, a deep learning-based 2-D GPR forward solver is proposed to predict the GPR B-scans of subsurface objects buried in the heterogeneous soil. The proposed solver is constructed as a bimodal encoder–decoder neural network. Two encoders followed by an adaptive feature fusion module are designed to extract informative features from the subsurface permittivity and conductivity maps. The decoder subsequently constructs the B-scans from the fused feature representations. To enhance the network’s generalization capability, transfer learning is employed to fine-tune the network for new scenarios vastly different from those in training set. Numerical results show that the proposed solver achieves a mean relative error of 1.28%. For predicting the B-scan of one subsurface object, the proposed solver requires 12 ms, which is less than the time required by a classical physics-based solver.