We investigate possibilities of solar coronal heating by acoustic waves generated not in the photosphere but in the corona, focusing on heating in the mid-to low-latitude corona, where the low-speed wind is expected to come from. Acoustic waves of period $ 100 s are triggered by chromospheric reconnection, one model of small-scale magnetic reconnection events recently proposed by Sturrock. These waves, having a finite amplitude, eventually form shocks to shape sawtooth waves (N-waves) and directly heat the surrounding corona by dissipation of their wave energy. Outward propagation of the N-waves is treated based on weak-shock theory, so that the heating rate can be evaluated consistently with physical properties of the background coronal plasma without setting a dissipation length in an ad hoc manner. We construct coronal structures from the upper chromosphere to outside 1 AU for various acoustic wave inputs, with a range of energy flux of F w;0 ¼ ð1 20Þ Â 10 5 ergs cm À2 s À1 and a period of ¼ 60-300 s. The heating by the N-wave dissipation works effectively in the inner corona, and we find that waves of F w;0 ! 2 Â 10 5 ergs cm À2 s À1 and ! 60 s could maintain the peak coronal temperature, T max > 10 6 K. The model could also reproduce the density profile observed in the streamer region. However, due to its short dissipation length, the location of T max is closer to the surface than in observation, and the resulting flow velocity of the solar wind is lower than the observed profile of the low-speed wind. Cooperation with other heating and acceleration sources with larger dissipation lengths are inevitably needed to reproduce the real solar corona.