The taking theory of U.S.A. is between legal encroachment with compensation (eminent domain) and legal encroachment without compensation (police power), as a compensation system to fill up the encroachment of ”violation of laws without responsibility” so as to protect private property. Compensation is one of the remedies to the damage of civial welfare which can be divided into such two kinds as remedy before taking judgment and remedy after taking judgment. The remedy before taking judgment is judicial review while the remedy after taking judgment is to announce control measures to be invalid, or in applying administrative remedial measures or providing monetary compensation, with the objective to help the property encroached under taking to recover to the value before encroachment of taking. This paper is to study that as private property right encounters encroachment of taking, how to remedy in accordance with American laws to ensure the property right, and discuss if there are matters for reference to the remedy of property taking of our nation.