We present 10 new transit light curves of the transiting hot Jupiter HAT-P-13b, obtained during two observational seasons by three different telescopes. When combined with 12 previously published light curves, we have a sample consisting of 22 transit light curves, spanning 1041 days across four observational seasons. We use this sample to examine the recently observed large-amplitude transit timing variations (TTVs) by Pál et al. and give refined system parameters. We find that the transit times are consistent with a linear ephemeris, with the exception of a single transit time, from UT 2009 November 5, for which the measured mid-transit time significantly deviates from our linear ephemeris. The nature of this deviation is not clear, and the rest of the data do not show any significant TTVs.United States. National Aeronautics and Space Administration (award NNX09AB33G)