The beam four-dimensional transverse phase-space density distribution (4D-TPSD) is an important physical quantity in beam dynamic. Except the 2-D emittance (a kind of its reducing form), which is commonly measured in a precision of ten percent, there is no way to measure the 4D-TPSD up to now according to my knowledge. In this paper, a method of measuring 4D-TPSD is proposed. Based on the 4-D Radon transform, a section of linear transporting line with two adjustable independent complete parameters (for example, a set of F,D quadrupoles) can be used as the equipment for measuring 4D-TPSD. Because this method is a kind of digital processing as similar to the CT (Computerized Tomography), the precision of the resulted 4D-TPSD will be satisfied for variety of applications (basic researching or