A novel method to design highly uniform axial coils inside a closed magnetically shielded cylinder (MSC) is presented. The proposed method has two major advantages over existing methods. First, based on the coupling model of coil and MSC with finite permeability and finite thickness, the image method and target-field method (TFM) are introduced to provide a flexible design method for the coil inside the MSC. Second, a backpropagation neural network (BPNN) model and particle swarm optimization (PSO) algorithm are used to predict and optimize the coil parameters, thus reducing the magnetic field deviation caused by the use of discrete wires to approximate the continuous current density. Simulations indicate that this method reduces the magnetic field deviation within the target region from $2.63 \times 10^{-3}$ to $1.13 \times 10^{-4}$ compared with the coils designed using the TFM without consideration of the coupling effect. The magnetic field deviation is reduced from $1.42 \times 10^{-4}$ to $1.13 \times 10^{-4}$ compared with the coils designed in the ideal magnetic conductor. Moreover, the field deviation is reduced to $2.43 \times 10^{-5}$ after optimization using the BPNN and PSO methods. The experimental results also verify the effectiveness of the design method and its practicability in compensating for the residual field of the MSC. The method proposed in this research has major significance for the establishment of practical magnetoencephalography and magnetocardiography measurement systems.