Laser trapping is a widely used technique such as manipulating cells. Recently the trapping technique is used in air, for example, a precision probe for sensing the surface of an object. To expand the applications of the trapping technique in air, more experimental investigations need to be implemented for properties such as trapping forces. We studied the dynamic properties of a micro-sphere (f8um) optically trapped in air by using a radially or linearly polarized beam. Firstly in order to predict the trapping forces working on a micro-sphere, the forces are analyzed by a ray-tracing method. The results show that an axial force of radial polarization is larger than one of linear polarization. Considering the radial forces, the force of radial polarization is smaller than one of linear polarization. These results can be understood by noting forces generated by p- and s-polarization. Secondly, we examine the trapping efficiency in optical trapping experimentally. Radial trapping efficiency is evaluated by measuring a spring constant. Experimental results and simulated results are in good agreement that the linear polarized beam achieved a 1.25 times higher spring constant than radial polarization. Axial trapping efficiency is examined by measuring minimum trapping laser power. Experimental results are one tenth underestimated although qualitatively they are coincident. Radial polarization is shown to be approximately 2 times higher than linear polarization. Thus, employing radial polarization, the optical trapping of the glass microsphere in air is achieved by using an objective lens with NA0.80.