This paper describes a novel algorithm for recovering time-domain signal from quantized amplitude and phase spectrogram, which is applicable for spectrogram-based audio coding. In order to obtain a better quality sound, a phase reconstruction technique is first applied with constraint for keeping phase in each time-frequency bin within each quantization range, and then, time-domain signal is recovered by the standard inverse short-time Fourier transform. Experimental evaluation based on the objective PEAQ measure shows that the proposed range-constrained phase reconstruction is effective for improving the sound quality.