We present a computationally efficient real-time algorithm for constructing audio signals from spectrograms. Spectrograms consist of a time sequence of short time Fourier transform magnitude (STFTM) spectra. During the audio signal construction process, phases are derived for the individual frequency components so that the spectrogram of the constructed signal is as close as possible to the target spectrogram given real-time constraints. The algorithm is a variation of the classic Griffin and Lim [1] technique modified to be computable in real-time. We discuss the application of the algorithm to time-scale modification of audio signals such as speech and music, and performance is compared with other methods. The new algorithm generates comparable or better results with significantly less computation. The phase consistency between adjacent frames produces excellent subjective sound quality with minimal fame transition artifacts.