Channel estimation is a challenging problem for realizing efficient ambient backscatter communication (AmBC) systems. In this letter, channel estimation in AmBC is modeled as a denoising problem and a convolutional neural network-based deep residual learning denoiser (CRLD) is developed to directly recover the channel coefficients from the received noisy pilot signals. To simultaneously exploit the spatial and temporal features of the pilot signals, a novel three-dimension (3D) denoising block is specifically designed to facilitate denoising in CRLD. In addition, we provide theoretical analysis to characterize the properties of the proposed CRLD. Simulation results demonstrate that the performance of the proposed method approaches the performance of the optimal minimum mean square error (MMSE) estimator with perfect statistical channel correlation matrix.