The process of fast magnetic reconnection driven by intense ultra-short laser pulses in underdense plasma is investigated by particle-in-cell simulations. In the wakefield of such laser pulses, quasi-static magnetic fields at a few mega-Gauss are generated due to nonvanishing cross product ∆(n /γ) × p. Excited in an inhomogeneous plasma of decreasing density, the quasi-static magnetic field structure is shown to drift quickly both in lateral and longitudinal directions. When two parallel-propagating laser pulses with close focal spot separation are used, such field drifts can develop into magnetic reconnection (annihilation) in their overlapping region, resulting in the conversion of magnetic energy to kinetic energy of particles. The reconnection rate is found to be much higher than the value obtained in the Hall magnetic reconnection model. Our work proposes a potential way to study magnetic reconnection-related physics with short-pulse lasers of terawatt peak power only