As a Canadian citizen, you have the absolute right to live and work in Canada. As a permanent resident of the United States, you have the right to permanently live and work in the US. So as long as you are physically in Canada or the US when you are working, you should be fine.Taxes will depend on where your tax home is, and it can be complicated. As a green card holder, you must file a US tax return no matter where in the world you live if US law requires it and as you work for a Canadian company, you may have to file a return in Canada if you live in Canada and/or have Canadian income tax deducted from your pay.As another answer states, there is a treaty between Canada and the US in regards to income taxes, as well as one on social security. The goal of the treaties is to reduce or eliminate double taxation.If you think you can handle it yourself, visit both Agence du revenu du Canada (Canada Revenue Agency) and An official website of the United States government (Internal Revenue Service) and start reading. In the US I would start with Publication 519 - US Tax Guide for Aliens and the instructions for Form 1040 (the full form, not 1040A or 1040EZ.) For Canada, you should file either Form NR-73 (living in the US) or NR-74 (living in Canada) and they will make a residency determination. This determination will guide you on which tax package you have to file and which guide you need to read.If tax is really not your thing, then you need a professional who specializes in both countries. This will likely be expensive, but cheaper than interest and penalties if you get it wrong.Note that while I am experienced in this area as a lay person, I am not an accountant or tax attorney and none of the above should be considered to be professional advice.