Aiming at the weak voltage output signal of the magnetic adsorption strain sensor measuring clamping force, and the requirement of wide input range for signal conditioning circuit, a linear amplification circuit is designed. Depending on the numerical range of the output signal, the parameters of the circuit elements are determined, and the linear relationship between the input and the output is obtained. The circuit is characterized by changing the resistance associated with the slope and intercepting, the signal conditioning can be achieved for different sensitivity of the clamping force sensor. Constant current source circuit design ensures the linear relationship between input voltage and output current. In this paper, the clamping force sensor with the sensitivity of 0.4mV/V which is taken as an example, at 10V supply voltage, realizes the linear conversion of the voltage signal from 0–4mV to 4–20mA, meets the requirements of PLC acquisition system for input signal, and amplifies the weak voltage signal nearly1287 times. By comparing the conclusion of theoretical analysis and actual test, the feasibility of the design is further validated. Finally, the error analysis of the circuit is carried out, and the corresponding improvement measures are given.