When the number of the mixed signals is less than that of the source signals, the underdetermined blind source separation (BSS) is a significant difficult problem. Due to the fact that the great amount data of speech communications and real-time communication has been required, we utilize the intractability of the underdetermined BSS problem to present a dual key speech encryption method. The original speech is mixed with dual key signals which consist of random key signals (one-time pad) generated by secret seed and chaotic signals generated from chaotic system. In the decryption process, approximate calculation is used to recover the original speech signals. The proposed algorithm for speech signals encryption can resist traditional attacks against the encryption system, and owing to approximate calculation, decryption becomes faster and more accurate. It is demonstrated that the proposed method has high level of security and can recover the original signals quickly and efficiently yet maintaining excellent audio quality.