Both temporal and spatial characteristics of air plasma induced by tightly-focused laser pulse with central wavelength of 800 nm and pulse width of 50 fs are numerically simulated on the basis of a three-dimensional spatial ionization model with rotational symmetry, and the dynamic evolution of refractive index in whole plasma area is revealed. The simulation results clearly show that, when the laser pulse begins to focus, the ionization of air firstly appears in the region near the focal point. The initially ionized air gradually grows to form a water droplet-like plasma region with saturated electron density at the center and a high refractive index gradient in the peripheral. As the laser pulse propagates through the focal plane, the plasma zone expands forwards and forms an ionization region with almost symmetrical double-oval-shape. After the laser pulse propagates out of the focal region, the intensity of air plasma decreases along the direction of transmission and varnishes finally. Focused by a 10-fold microscope objective, the whole evolution process of the air plasma induced by laser pulse with pulse energy of 500 μJ and pulse width of 50 fs lasts about 3 ps. The simulation results can fit the experimental results obtained under low air pressure of 30 kPa.