In their recent paper [Phys. Rev. A 97, 062322 (2018)], Wan et al. proposed a quantum algorithm to solve systems of linear equations Ax = b, where A is an n × n Toeplitz matrix generated by the Fourier coefficients of a continuous, 2π-periodic, and positive function f . For large enough n, they claimed that the algorithm is valid for all b. In this Comment we prove that, in general, this is not true.