We detected 51 faint Jovian Trojan asteroids in the L4 Lagrangian swarm in survey observations near opposition and the ecliptic using a wide-field mosaicked CCD camera on the 8.2 m Subaru Telescope. We report the Trojan size distributions in this paper. The surveyed sky area was about 3 deg2 and located ~30° in longitude ahead of the L4 point. From trailed-image simulations of hypothetical Trojans, we measured the 90% complete detection limiting magnitudes for our Trojan asteroids on a CCD chip-by-chip basis. The limiting magnitudes varied by 0.4-0.5 mag between chips; therefore, we introduce a new measure of detection limit appropriate for multichip CCD cameras. By statistically comparing the observed number of Trojans with the predictions from theoretical size distributions near the limiting magnitude calculated in this way, we determined a limiting diameter of D~2 km, corresponding to the detection limit of this survey. On the other hand, the detected Trojans covered a size range of 0.7 km<D<12.3 km (with an assumed albedo of 0.04 for each object, which is the mean value of known Trojans thus far). Hence, we discuss the size distribution of the observed Trojans in the size range of 2 km<D<10 km. For this entire range, we found the mean slope of the cumulative size distribution, namely, the power-law distribution index, to be 1.9+/-0.1 this value is consistent with the 2000 estimate by Jewitt and coworkers. However, we noted a slight change in the slope of the cumulative size distribution at D~5 km. Therefore, we obtained separately fitted slopes for the size ranges of 2 km<=D<5 km and 5 km<D<=10 km of 1.3+/-0.1 and 2.4+/-0.1, respectively. This break in the slope of the size distribution has also been seen in the size distribution of kilometer to subkilometer main-belt asteroids (Yoshida and coworkers), and so we compared the size distributions of the two populations. Based on the surface distribution model of L4 Trojans proposed by Jewitt and coworkers, we estimated the total number of L4 Trojans with D>1 km. Finally, we discuss, from a cosmogonic viewpoint, a possible relation between Trojans and short-period comets on the basis of their size distribution slopes.Based on data collected at the Subaru Telescope, which is operated by the National Astronomical Observatory of Japan.