In this work, a low-complexity data-driven characterized-long-short-term-memory (C-LSTM)-aided channel modeling technique is proposed for optical single-mode fiber (SMF) communications. To fully utilize the sequence correlation learning ability of traditional long short-term memory (LSTM) networks and solve the gradient explosion problem, the feature information is introduced into the traditional LSTM input layer to better characterize the intersymbol interference caused by dispersion in SMF modeling. The simulation results show that the proposed C-LSTM can effectively alleviate the gradient explosion problem with a stable and ultimately lower mean square error (MSE) than traditional LSTM. Compared with the split-step Fourier method (SSFM) and the conditional generative adversarial network (CGAN), the proposed C-LSTM has superior computational complexity. Moreover, due to the sequence correlation learning ability inherent to C-LSTM, coupled with the flexibility of feature information selection, the proposed C-LSTM-aided modeling technique has a higher modeling accuracy than traditional LSTM. Moreover, the C-LSTM-aided modeling technique can be effectively extended to other channel modeling applications with strong sequence correlations.