We demonstrate the wide-band (> 25-nm) long-distance (> 1000-km) chromatic dispersion compensation by midway spectral inversion (MSI) using a periodically-polled LiNbO3 device. In order to achieve a flat zero net dispersion, the fourth order dispersion of the single-mode fibers is canceled by MSI, while the third order dispersion is compensated for by the negative slope dispersion compensation fiber (NS-DCF). The second order dispersion is canceled out by both. The long distance propagation is realized by a double recirculation-loop system. A very flat zero dispersion is measured for the first time for over 1000-km single-mode fiber propagation with MSI dispersion compensation.