We report the discovery of GeV gamma-ray emission from the molecular cloud complex that surrounds the supernova remnant (SNR) W44 using the Large Area Telescope on board Fermi. In addition to the GeV emission from SNR W44, which shows the characteristic pion-decay spectral feature and is likely to arise from the dense radio-emitting filaments within the remnant, the gamma rays that appear to come from the surrounding molecular cloud complex can be ascribed to the cosmic rays that have escaped from W44. Morphology of the large-scale gamma-ray emission suggests bi-polar diffusion from the SNR, in agreement with recent theoretical prediction. We will discuss the gamma-ray production processes by trapped and escaped cosmic rays.