We present 12 new transit light curves of the hot-Jupiter TrES-3b observed during 2012-2018 to probe the transit timing variation (TTV). By combining the midtransit times determined from these 12 transit data with those reestimated through uniform procedure from 71 transit data available in the literature, we derive new linear ephemeris and obtain the timing residuals that suggest the possibility of TTV in the TrES-3 system. However, the frequency analysis shows that the possible TTV is unlikely to be periodic, indicating the absence of an additional body in this system. To explore the other possible origins of TTV, the orbital decay and apsidal precession ephemeris models are fitted to the transit time data. We find the decay rate of TrES-3b to be (P) overt dot(q) = -4.1 +/- 3.1 ms( )yr(-1), and the corresponding estimated modified stellar tidal quality factor of Q(*)' similar to 1.11 x 10(5) is consistent with the theoretically predicted values for the stars hosting the hot-Jupiters. The shift in the transit arrival time of TrES-3b after 11 years is expected to be T-s(hift) similar to 69.55 s, which is consistent with the rms of the timing residuals. Besides, we find that the apsidal precession ephemeris model is statistically less probable than the other considered ephemeris models. It is also discussed that despite the fact that the linear ephemeris model appears to be the most plausible model to represent the transit time data, the possibility of the orbital decay cannot be completely ruled out in the TrES-3 system. To confirm this, further high-precision and high-cadence follow-up observation of transits of TrES-3b would be important.