This paper presents a new maximum power point tracking (MPPT) technique for extracting the maximum power in thermoelectric generator (TEG) systems. Considering the linear nature of I-V characteristics of a TEG source, the proposed technique is based on the linear extrapolation principle. The I-V coordinates of two random operating points are used in computing the coordinates of new MPP. As anticipated, the proposed method involves only three sampling periods to reach the MPP under any dynamic conditions. The linear extrapolation-based MPPT technique has several advantages such as simplicity of analysis, fixed and minimal convergence time, ease of implementation and a high tracking efficiency due to the absence of steady-state oscillations. Further, there is no need to interrupt the circuit for measuring the open-circuit voltage of TEG. Also, there is no requirement for additional switches or components. The simulation and test results show that the proposed algorithm has a superior performance as compared to that of the perturb and observe algorithm.