We fabricated an asymmetric long-period grating (LPG) by periodically tapering a section of standard single-mode fiber using a resistive filament heating. The LPG exhibits large peak transmission attenuation of -30.31 dB with only 22 periods in a 1.0 cm long optical fiber and possesses unique characteristics for sensing applications. The bending and strain sensitivities are 1.74 nm m and 1.11 pm/mu epsilon, respectively. The polarization dependent loss is large, up to 11.65 dB, which is caused by an asymmetric index profile in the cross section of the tapered LPG.