In general, pension income is taxed according to where you worked when you (or the employer) made the contributions. Your pension is still "effectively connected" to the US and considered US taxable income, even if you are withdrawing the pension overseas. The pension plan must generally withhold 30% of any payout.
https://www.irs.gov/retirement-plans/plan-distributions-to-foreign-persons-require-withholding
To answer more specifically, you would need to tell us exactly what you mean by "private pension" -- company pension, IRA, 401k, etc. If your contributions were taxable, only the earnings should be taxed now, but if the company made contributions, they are almost certainly non-taxed at the time and fully taxable now. We also need to know what country you are a resident or citizen of, because there may be a tax treaty that will affect the answer. @pk
