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The predictor–corrector (P–C) method applies linear interpolation technique to calculate Volterra integral equations equivalent to the considered fractional differential equations (FDEs). This paper reveals that, the relative error approaches a certain value but not infinitesimal even as the step size decreases to zero for certain FDEs. In these equations, the integrated function has a zero value and an infinite (or infinitesimal) slope at the origin. The interpolation technique is responsible for the non-diminishing relative error. Based on this analysis, we modify the P–C method by employing an alternative interpolation strategy to reduce the relative error. Numerical examples show the modified method can provide much more accurate approximations not only near the origin but also over the whole solution domain. [ABSTRACT FROM AUTHOR]