The charged Higgs production associated with a W± boson has a smooth cross-section as a function of the charged Higgs mass at muon colliders. The cross-section in minimal supersymmetric standard model (MSSM) is about 25 fb in the range 200 GeV < mH± <400 GeV with tan β = 50. This is much larger than the corresponding cross-section at an e+e- collider which reaches a fraction of femtobarn. The observability of this charged Higgs production at a muon collider has been recently studied in an earlier work leading to the result that with 1 ab-1, a 5σ signal can be observed throughout the aforementioned mass range. In this paper, results of a study based on a general two Higgs doublet model (types II and III) are presented and the cross-section of the charged Higgs production in the most sensitive parameter space is evaluated. It is concluded that the cross-section increases with increasing neutral Higgs boson masses involved in the s-channel diagram and can be as large as several picobarn with tan β = 50. The region of "physical Higgs boson mass" parameter space which could lead to a 5σ signal at 50 fb-1 is specified.