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In the studies of unit commitment or optimal power flow, to formulate a mixed-integer linear programming model that can be efficiently solved with commercial solvers, it is necessary to approximate the quadratic cost curves of thermal units as piecewise linear (PWL) functions. The conventional approach involves evenly spaced piecewise linear (ES-PWL) interpolation, which often results in relatively large approximation errors. In order to reduce the error, this paper proposes a more accurate PWL method for approximating the quadratic cost functions of thermal units. The method employs a linear least-squares fit instead of linear interpolation within each subinterval and introduces a one-terminal-constraint approach to ensure the continuity of the piecewise function. Subsequently, a straightforward equation is derived, applicable to the widely used ES-PWL interpolation, with the potential to enhance the accuracy of the approximation. Mathematical verification attests that the proposed method substantially diminishes the squared 2-norm error, less than 37.5% of the error associated with ES-PWL interpolation. Subsequent numerical investigations are carried out on a 10-unit system, the IEEE RTS-79, and a real industrial system. The findings validate that all the approximation errors of the proposed method are within 37.5% of the errors associated with the ES-PWL interpolation, meaning that a unit commitment solution that closely approximates the outcome of the quadratic function is obtained. The computational time is also acceptable. [ABSTRACT FROM AUTHOR]