Strain estimation is vital in phase-sensitive optical coherence elastography (PhS-OCE). In this Letter, we introduce a novel, to the best of our knowledge, method to improve strain estimation by using a dual-convolutional neural network (Dual-CNN). This approach requires two sets of PhS-OCE systems: a high-resolution system for high-quality training data and a cost-effective standard-resolution system for practical measurements. During training, high-resolution strain results acquired from the former system and the pre-existing strain estimation CNN serve as label data, while the narrowed light source-acquired standard-resolution phase results act as input data. By training a new network with this data, high-quality strain results can be estimated from standard-resolution PhS-OCE phase results. Comparison experiments show that the proposed Dual-CNN can preserve the strain quality even when the light source bandwidth is reduced by over 80%.