By utilizing the 1m and 2.4m telescopes of Yunnan Observatories, we obtained 13 new photometric transit light curves of WASP-12 exoplanetary system from 2009 to 2016. The data were analysed by using the Transit Analysis Package with the aid of Markov chain Monte Carlo technique. Based on the physical parameters from previous work, we have obtained the variation of radius with wavelength and mid-transit times of WASP-12b. Compared with a set of theoretical transmission spectra, its radius variation is almost consistent with a flatten and featureless model along with a slope in the bluer band, except the weak Na signal. The flatten and featureless transmission spectrum implies a possible evidence for the absence of TiO and VO in the upper atmosphere of WASP-12b. The slope in the bluer band may result from the Rayleigh scattering caused by H-2/He and there would be hazes or hydride in the upper atmosphere. Combined new mid-transit times with all of the available timing data in literature, we have found that there is a significant change in the planetary orbit, the residuals of the timing prefer the orbital decay model to the apsidal precession model and the planetary interaction-induced TTV model. We updated the decay rate as -37.14 +/- 1.31 ms yr(-1) and derived a slightly lower modified quality factor Q(*)' for the constant-phase lag model. Furthermore, the current observations cannot rule out the planetary interaction-induced TTV model conclusively.