+1(514) 937-9445 or Toll-free (Canada & US) +1 (888) 947-9445
I am not 100% certain, but very confident, that you can still enter the U.S. even after your visa expired as long as your I-94 is valid. When we were F-1 students we were allowed to do that; I had friends who made quick visits to Mexico and Canada and since they didn't surrender their I-94s, they were allowed to enter on expired visas, though they were told that if they went back to their home countries their I-94s would be taken and they would have to get new visas.

Either way, I believe you should be able to just drop off the I-94s to the Canadian officers at the border. You might want to check with the CBSA just to be sure. If they are not cooperative, the procedures for having everything recorded is at:

https://help.cbp.gov/cgi-bin/customs.cfg/php/enduser/std_adp.php?p_faqid=752&p_created=1077641280&p_sid=EudXOuOj&p_accessibility=0&p_redirect=&p_srch=1&p_lva=&p_sp=cF9zcmNoPTEmcF9zb3J0X2J5PSZwX2dyaWRzb3J0PSZwX3Jvd19jbnQ9MTEsMTEmcF9wcm9kcz0mcF9jYXRzPSZwX3B2PSZwX2N2PSZwX3BhZ2U9MSZwX3NlYXJjaF90ZXh0PUktOTQ~&p_li=&p_topview=1

(credit to someone else who once posted this link on the forum, but whose name I can't remember)

Since you would have a stamp showing you entered and landed in Canada, a copy of that would easily prove that you left the U.S.A. in time.

Suin said:
by that time my visa will be already expired, I will not be allowed to enter the US. is it possible just to drive to the Canadian customs and give it up there?
thank you
 
actually they didn't stamp my passport at Canadian side. just issued COPR, nothing else.
 
Very strange! Then you would have to send other evidence like shown in the link if you don't turn in the I-94 on time.

Suin said:
actually they didn't stamp my passport at Canadian side. just issued COPR, nothing else.