Signal compression is crucial for resource-constrained wireless neural recording applications with limited data bandwidth, and Compressed Sensing (CS) has successfully demonstrated its potential in this field. However, the conventional CS approaches rely on data-dependent and computationally intensive dictionary learning processes to find out the sparse representation of neural signals, and dictionary re-training is inevitable during real experiments. This paper proposes a training-free CS approach for wireless neural recording. By adopting the analysis model to enforce the signal sparsity and constructing a multi-order difference matrix as the analysis operator, it avoids the dictionary learning procedure and reduces the need for previously acquired data and computational complexity. In addition, a group weighted analysis 11-minimization method is developed to recover the neural signals. Experimental results reveal that the proposed approach outperforms the state-of-the-art CS methods for wireless neural recording.