  Let $F^{2,m}(\mathbb{C})$ denote the Fock-Sobolev space of complex plane. In
this paper, we characterize the semi-commutator of two Toeplitz operators on
$F^{2,m}(\mathbb{C})$ is zero. The result is different from the result of
Bauer, Choe, and Koo. (J. Funct. Anal., 268 (2015): 3017-3060.)
