We present an independent catalog (FRIIRGcat) of 45241 Fanaroff-Riley Type II (FR-II) radio galaxies compiled from the Very Large Array Faint Images of the Radio Sky at Twenty-centimeters (FIRST) survey and employed the deep learning method. Among them, optical and/or infrared counterparts are identified for 41,425 FR-IIs. This catalog spans luminosities 2.63x10^22^<=Lrad<=6.76x10^29^W/Hz and redshifts up to z=5.01. The spectroscopic classification indicates that there are 1431 low-excitation radio galaxies and 260 high-excitation radio galaxies. Among the spectroscopically identified sources, black hole masses are estimated for 4837 FR-IIs, which are in 10^7.5^<~M_BH_<~10^9.5^M_[sun}_. Interestingly, this catalog reveals a couple of giant radio galaxies (GRGs), which are already in the existing GRG catalog, confirming the efficiency of this FR-II catalog. Furthermore, 284 new GRGs are unveiled in this new FR-II sample; they have the largest projected sizes ranging from 701 to 1209kpc and are located at redshifts 0.31<z<2.42. Finally, we explore the distribution of the jet position angle and it shows that the faint Images of the FIRST images are significantly affected by the systematic effect (the observing beams). The method presented in this work is expected to be applicable to the radio sky surveys that are currently being conducted because they have finely refined telescope arrays. On the other hand, we are expecting that further new methods will be dedicated to solving this problem.