The mechanism of solar coronal heating has been unknown since the discovery that the coronal plasma temperature is a few million degrees. There are two promising mechanisms, the Alfvén wave model and the nanoflare-reconnection model. Recent observations favor the nanoflare model since it readily explains the ubiquitous small-scale brightenings all over the Sun. We have performed magnetohydrodynamic (MHD) simulations of the nonlinear Alfvén wave coronal heating model that include both heat conduction and radiative cooling in an emerging flux loop and found that the corona is episodically heated by fast-and slow-mode MHD shocks generated by nonlinear Alfvén waves via nonlinear mode-coupling. We also found that the time variation of the simulated extreme-ultraviolet and X-ray intensities of these loops, on the basis of the Alfvén wave model, is quite similar to the observed one, which is usually attributed to nanoflare or picoflare heating. This suggests that the observed nanoflares may not be a result of reconnection but in fact may be due to nonlinear Alfvén waves, contrary to current widespread opinion.