I should be grateful if you would is this correct grammar?

The phrase "I should be grateful if you would" is grammatically correct, but it is not a complete sentence. It needs to be followed by a verb to form a complete thought. For example:

* I should be grateful if you would help me with this task.

* I should be grateful if you would let me know your decision.

Make sure to complete the sentence with the appropriate verb and you'll be good to go!