This paper presents a speech encryption scheme by performing a combination of modified chaotic maps inspired by classic logistic and cubic maps. The main idea was to enhance the performance of classical chaotic maps by extending the range of the chaotic parameter. The resulted combining map was applied to a speech encryption scheme by using the confusion and diffusion architecture. The evaluation results showed a good performance regarding the chaotic behaviors such as initial value, control parameter, Lyapunov exponent, and bifurcation diagram. Simulations and computer evaluations with security analysis showed that the proposed chaotic system exhibits excellent performance in speech encryption against various attacks. The results obtained demonstrated the efficiency of the proposed scheme compared to an existing valuable method for static and differential cryptographic attacks.