Lightweight neural networks are a special type of neural networks which can operate efficiently through resource consumption optimization in resource-constrained environments. Their training process usually aims to optimize the overall performance. However， in practical applications， such a trained neural network sometimes suffers from low classification accuracy for some classes of interest， which are more important to users or applications than others. To address this problem， a structural fine-tuning method for lightweight neural networks—Synaptic join method based on the sub-minimum value threshold （SMVT-SJ） is proposed. This method defines the threshold for new synaptic weights using the second-smallest value strategy and selectively improves the classification accuracy for the target class by adding a small number of cross-layer synapses from hidden layers to the corresponding output neuron. In order to select more efficient new synapses， the SMVT-SJ method proposes a synaptic evaluation process to evaluate the performance of each candidate synapse according to the distribution of all possible appropriate weights. Experimental results on different datasets show that the proposed method can effectively enhance the classification accuracy of specific target class and maintain the overall accuracy without a significant decrease， and has good generalization and robustness.