We studied the pressure effects on the electronic and structural properties of LaOFeAs by first-principles calculations. For the anti-ferromagnetic (AFM) phase with stripelike aligned Fe spins, the electronic density of states at the Fermi level (N (E F )) slightly descends first with increasing applied pressure, then bounces up with further increasing pressure (or decreasing volume), and reaches its maximum at ~ 29.2 GPa with the volume ~ 80% of the ambient pressure value (V 0 ). Similar behavior is expected in the physical quantities that are proportional to N (E F ), such as the electronic specific heat and the Pauli paramagnetic susceptibility. At this volume (V = 0.8V 0 ), the LaOFeAs crystal undergoes a structural phase transition from the orthorhombic structure to the tetragonal one, which is accompanied by the disappearance of the long-ranged AFM order.