Traditional low bit-rate speech coding approach only handles narrowband speech at 8kHz, which limits further improvements in speech quality. Motivated by recent successful exploration of deep learning methods for image and speech compression, this paper presents a new approach through vector quantization (VQ) of mel-frequency cepstral coefficients (MFCCs) and using a deep generative model called WaveGlow to provide efficient and high-quality speech coding. The coding feature is sorely an 80-dimension MFCCs vector for 16kHz wideband speech, then speech coding at the bit-rate throughout 1000-2000 bit/s could be scalably implemented by applying different VQ schemes for MFCCs vector. This new deep generative network based codec works fast as the WaveGlow model abandons the sample-by-sample autoregressive mechanism. We evaluated this new approach over the multi-speaker TIMIT corpus, and experimental results demonstrate that it provides better speech quality compared with the state-of-the-art classic MELPe codec at lower bit-rate.