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 Pal et al. (2011MNRAS.413L..43P) 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.