Video quality assessment is one of the key techniques in video communication and editing. With constraints of transmission system, storage space etc., original information of videos may not be available. No-reference video quality assessment (NRVQA) methods are in demand. This paper presents a reconstruction-based no-reference video objective quality assessment algorithm for quantization distorted video frames. The proposed assessment is performed without any prior information of distortion or codec parameters. By deeply mining the features of the testing frames, the proposed algorithm can reconstruct zero coefficients' values in every sub-band of frequency coefficients. In addition, non-zero frequency coefficients error will be estimated more accurately with the proposed modified DCT coefficients distribution model. To fully evaluate the proposed NRVQA algorithm, testing video frames are distorted with various quantization steps blindly. Experimental results have showed that the proposed reconstruction-based NRVQA algorithm can give out pleasant performances compared with the state of the art NRVQA algorithms.