Deep neural networks for medical image reconstruction are traditionally trained using high-quality ground-truth images as training targets. Recent work onNoise2Noise (N2N) has shown the potential of using multiple noisy measurements of the same object as an alternative to having a ground truth. However, existing N2N-based methods cannot exploit information from various motion states, limiting their ability to learn on moving objects. This paper addresses this issue by proposing a novel motion-compensated deep image reconstruction (MoDIR) method that can use information from several unregistered and noisy measurements for training. MoDIR deals with object motion by including a deep registration module jointly trained with the deep reconstruction network without any ground-truth supervision. We validate MoDIR on both simulated and experimentally collected magnetic resonance imaging (MRI) data and show that it significantly improves imaging quality.