I am a U.S. resident living in the U.S. and I own a foreign company. I pay taxes on that income in the foreign country. Should that income also get taxed in the U.S.?

All total worldwide income must be reported on a US income tax form.  If you pay taxes in another country  then you can take the foreign tax credit or a Sch A deduction. 

You can use TurboTax from anywhere in the world to complete a US tax return.

See this TurboTax support FAQ - https://ttlc.intuit.com/questions/1900705-can-i-e-file-with-a-foreign-address

See this TurboTax support FAQ for reporting foreign earned income - https://ttlc.intuit.com/questions/1895445-do-i-need-to-report-foreign-income

This IRS Publication 54 Tax Guide for U.S. Citizens and Resident Aliens Abroad has a wealth of information - https://www.irs.gov/pub/irs-pdf/p54.pdf

@aguila-fernando9 , whereas I completely agree with @Critter-3  comments to your post, you have not told us what type pf entity ( sole proprietor, LLC, SA, C-Corp , partnership etc. etc. ), in which country and organized under which country' s laws. are you a citizen of that country, do you have an entity here in the USA that owns the foreign entity etc. etc.  Because , @Critter-3  answers are absolutely correct if we assume  certain  items   -- you a US person, you are the sole proprietor of an sole proprietor ship in another country ( assuming that the laws of that foreign country are pretty similar  to those of US) and US has tax treaty covering business  taxation etc.  Therefore we need to know more about the situation here .  Even though I suspect that @Critter-3 's assumptions are correct, still ......