That size sounds like it might be too large for the post office. However, if you can divide it into smaller boxes, then sending via surface mail can be reasonable.
If you can't make it any smaller, Yamato UPS may have a cheapish sea freight shipping option for self-packed boxes. I used this to move my personal effects from the UK to Japan about 10 years ago. (The sales people tried to sell me their gold-plated international removals service, but eventually gave me this option when I convinced them what a cheapskate I was). It took a couple of months. IIRC, they told me that the service was designed to serve students who were studying abroad, so you might get to the point more quickly if you ask them if they have a service for students.
You should also check the procedures for importing unaccompanied luggageto the US. Depending on what you're sending / why / how old it is etc. some items may be liable for customs charges etc.