It sure looks like an Ithaca Model 37 all tricked up, BUT....
It is more likely a Savage Stevens 350 Pump with ghost ring sights, #18951 (the current production sold by Savage Stevens). These were originally imported into the US by IAC (International Arms Corporation) around 2004, and might still be brought into this country by IAC and sold thru the Stevens name.
http://www.savagearms.com/firearms/models/ scroll down to SHOTGUNS
I think its made by Norinco and is a copy of the Ithaca 37.
More on IAC...
" Our business was founded in 1960 by Marty and Saul Arnstein. Their original retail gun shop, know as Ivanhoe Sports Center, was located in Watertown, Massachusetts and remained open for twenty five years.A wholesale division was formed in 1974 and today is known as Interstate Arms Corp, a leading distributor supplying retail gun shops nationwide with firearms and accessories. IAC IMPORTS is a division of Interstate Arms Corp that imports quality reproductions of classic firearms for distribution through some of America's leading wholesale distributors. "
Hope this helped.
From what I've been told some of these china knockoffs are pretty damn good quality long guns. Might be a lil rough looking all over but with some spit and polish can be made extremly reliable. YMMV as usual. I know some reenactors that use the chinese ones as replica trench booms so they can leave their real ones back home safe and sound.
I also think I remember someone telling me once those Stevens 350s don't have the slamfire functionality that an actual Ithaca 37 would have had.