Based on optical wave space-time duality theory, time lens and principle of optical pulse transmission in dispersive media are studied. A method have been proposed using pulses′ spectral envelope to transmit optical signals. With the fact that pulses′ spectral envelope will keep unchanged when propagating in dispersive medias, at the transmitter, an all-optical inverse Fourier transformation device based on time lens is used to transform the spectral envelope into time-domain, and a new transmitting symbol is obtained. An corresponding Fourier transformation device will be placed to recover original signals at the receiver. The transmission system presented can eliminate the chromatic dispersion, polarization mode dispersion (PMD), timing jitter and other liner distortions. Detailed implementations of optical Fourier transformation and inverse Fourier transformation are given. Besides, a 10 Gb/s-200 km optical transmission experiment without any dispersion compensations or pre-chirp verifies our transmission scheme, which offers a new method in high-speed optical communications.