Magnetorheological dampers (MRDs) are intelligent devices for semi-active control and are widely applied in vibration isolation. A high-fidelity modeling method is necessary to take full advantage of the controllable properties of MRDs. Therefore, a nested long short-term memory (NLSTM)-convolutional neural network-efficient channel attention (NLCE) modeling method based on a dual-flow neural network architecture is proposed herein. It uses the time, current, amplitude, frequency, displacement, and velocity as inputs and the damping force as the output. Extensive sinusoidal excitation experiments were conducted using a materials test system and two datasets (large and small sample numbers) were obtained. Five testing sets with different emphases were obtained from different experimental series. Four evaluation indexes were used for a quantitative comparison. First, after training with the large sample dataset, network ablation and comparison experiments were conducted based on a testing set-1. The mean absolute relative error (MARE) evaluation index decreased by 2.290% relative to that of the NLSTM (baseline), indicating that the NLCE method is optimal for predicting the motion characteristics of MRDs. Furthermore, after training with the small sample dataset, comparison experiments were conducted based on testing set-1 and testing set-2. The MAREs decreased by 3.984% and 0.871% relative to that of the NLSTM (baseline), respectively, indicating that the NLCE is also the best modelling method for small sample dataset. The visualization results from the above experiments verified the abilities of the NLCE modeling method for small sample-adaptation, fighting randomness, and identifying similarities. Finally, based on testing set-3, testing set-4 and testing set-5, the NLCE model trained with small sample datasets has high prediction accuracy in predicting the peak damping force (MAREs = 1.456%, 0.880%, and 1.482%, respectively), indicating a high prediction accuracy in the non-hysteretic region. Combining all of the experimental results shows that the NLCE is an effective method for predicting the motion characteristics of MRDs.