A kind of linerly tapered microstructure fiber has been proposed in this paper. The central wavelength, which is located in the anomalous dispersion region, is 1550 nm. We use an adaptive split-step Fourier method to numerically study the propagation of 1 ps laser pulse in this microstructure optical fiber. For the tapered fiber under consideration, a compression factor of 56.9 and a quality factor of 27 can be achieved in a fiber 1 m long. With the pulse shape evolution in the fiber, we find that in anomalous dispersion region, the pulse can be highly efficiently compressed by the increasing of nonlinearity coefficient and the decreasing of dispersion coefficient. Compared with the normal photonic crystal fibers, the thicker end of the tapered fiber is apt to be coupled to the laser pulse which has a larger effective mode area.