In time-varying flat-fading environments, time domain channel correlations are required for accurate channel estimation and interpolation. However, the correlation property, which depends on the Doppler spread, is hard to be extracted from corrupted channel responses within a short channel estimation interval. In this work, based on an approximate channel model via the Taylor expansion, we propose a joint channel and Doppler spread estimation scheme over time-varying flat-fading channels. It employs the expectation-maximization (EM) algorithm to iteratively attain the maximum-likelihood (ML) channel and Doppler spread estimates. Simulation results show that the proposed scheme achieves accurate performance of both channel estimation and Doppler spread estimation within a short estimation interval.