An all-fiber normal-dispersion Yb-doped fiber laser with 45°-tilted fiber grating (TFG) is, to the best of our knowledge, experimentally demonstrated for the first time. Stable linearly-chirped pulses with the duration of 4 ps and the bandwidth of 9 nm can be directly generated from the laser cavity. By employing the 45° TFG with the polarization-dependent loss of 33 dB, output pulses with high polarization extinction ratio of 26 dB are implemented in the experiment. Our result shows that the 45° TFG can work effectively as a polarizer, which could be exploited to single-polarization all-fiber lasers.