Reconstructing natural speech from neural activity is vital for enabling direct communication via brain-computer interfaces. Previous efforts have explored the conversion of neural recordings into speech using complex deep neural network (DNN) models trained on extensive neural recording data, which is resource-intensive under regular clinical constraints. However, achieving satisfactory performance in reconstructing speech from limited-scale neural recordings has been challenging, mainly due to the complexity of speech representations and the neural data constraints. To overcome these challenges, we propose a novel transfer learning framework for neural-driven speech reconstruction, called Neural2Speech, which consists of two distinct training phases. First, a speech autoencoder is pre-trained on readily available speech corpora to decode speech waveforms from the encoded speech representations. Second, a lightweight adaptor is trained on the small-scale neural recordings to align the neural activity and the speech representation for decoding. Remarkably, our proposed Neural2Speech demonstrates the feasibility of neural-driven speech reconstruction even with only 20 minutes of intracranial data, which significantly outperforms existing baseline methods in terms of speech fidelity and intelligibility.