1. An expansion read-only memory (ROM) management system, comprising: at least one computer host; and a management host connected with the at least one computer host through at least one bridge, wherein the management host comprises at least one virtual function and establishes at least one address lookup table to assign the at least one virtual function and at least one expansion ROM corresponding to the at least one virtual function to the at least one computer host, wherein each of the at least one address lookup table comprises a validity status, a computer host number, a virtual function address of a computer host end, a virtual function address of a management host end, a filter status, a filter range, and a corresponding at least one shadow register block, wherein the filter range represents a register address of the at least one expansion ROM, wherein the filter status in the at least one address lookup table is preset as “disable”, and when the at least one computer host transmits a write command to the management host, the management host sets the filter status in the at least one address lookup table to “enable” according to the write command, transfers the write command to the at least one shadow register block in the at least one address lookup table by software simulation, and performs an operation on the data in the corresponding at least one shadow register block and provides the data in the corresponding at least one shadow register block to the at least one computer host according to an operation result, when the at least one computer host issues a request to obtain a size of the at least one expansion ROM corresponding to the at least one virtual function, the management host provides data in at least one shadow register block corresponding to the at least one expansion ROM to the at least one computer host according to the at least one address lookup table, the at least one computer host assigns at least one memory block of the at least one computer host to the at least one expansion ROM according to the data in the at least one shadow register block, wherein when the at least one computer host issues a request to obtain data of the at least one expansion ROM through the at least one bridge, the management host provides the data of the at least one expansion ROM to the at least one computer host according to the at least one memory block.