The author introduces the concept of “bi-continuous” one-parameter semigroups of operators on Banach spaces, and then characterizes their generators by generalizing the Hille-Yosida theorem. The obtained result extends a result of J. R. Dorroh and J. W. Neuberger in [J. Funct. Anal. 136, No. 1, 114–126 (1996; Zbl 0848.22005)].