With the rise of direct-to-satellite mobile services, communication between high-orbit satellites and ground devices is becoming increasingly common. However, due to the increased communication distance, the rate of satellite voice calls has decreased. LPCNet encoders have become increasingly popular due to their effectiveness and high quality in speech synthesis. In this work, we propose a Gaussian mixture distribution LPCNet, where speech excitation employs a mixture of Gaussian distributions, predicting multiple consecutive excitation values independently at once, suitable for low bit-rate speech coding. We conducted tests on three open-source Chinese speech samples. Through subjective MUSHRA scoring, the improved approach showed a 5 \( \% \) increase in subjective listening ratings compared to the original LPCNet.