Have wage incomes in US and Canada, how to file tax?

[J1visa]

Dear all,

I am a dual PR of the US and Canada. I have income in Canada (T4) and income in the US (W2). I stay entire year in the US (without any day in Canada). I also pre-pay taxes in the US and Canada. Do you know how could I file tax returns? Can I file tax return in Canada first as a Canadian resident and do not let Canada know my income in the US, and then file tax return in the US ( I have to let the US know my income in Canada, that is law)? I try to do that way but now I have to pay tax for my income in both Canada and the US. Do you guy know something about tax treaty?

It is really complicated. Thanks for your help.