We perform transit timing variation (TTV) and transmission spectroscopy analyses of the planet HAT-P-37b, which is a hot Jupiter orbiting a G-type star. Nine new transit light curves are obtained and analyzed together with 21 published light curves from the literature. The updated physical parameters of HAT-P-37b are presented. The TTV analyses show a possibility that the system has an additional planet that induced the TTVs amplitude signal of 1.74{+/-}0.17minutes. If the body is located near the 1:2 mean-motion resonance orbit, the sinusoidal TTV signal could be caused by the gravitational interaction of a sub-Earth-mass planet with mass of 0.06M{Earth}. From the analysis of an upper-mass limit for the second planet, a Saturn-mass planet with orbital period less than 6 days is excluded. The broadband transmission spectra of HAT-P-37b favors a cloudy atmospheric model with an outlier spectrum in the B filter.