In this paper, a 2kb/s Waveform Interpolation speech coder is proposed based on non-negative matrix factorization (NMF). In characteristic waveforms (CWs) decomposition, band-partitioning initialization constraints were set to basis vectors before NMF was carried out. This decomposition method only requires speech signal from the current frame, and can yield high decomposition quality with low computational complexity. Besides, the high dimensional CWs matrix can be expressed by the low dimensional coding matrix, and this has facilitated the CWs quantization. The listening test shows that the proposed 2kb/s NMF-WI coder can give smooth speech with quality close to 2.4kb/s SVD-based WI coder.