Abstract: Given two points and their tangent vectors,this paper provides a method to construct a pleasing cubic Hermite curve satisfying the endpoint conditions.Firstly we supposes that the satisfactory curve exists with given endpoint conditions,and regards the magnitudes of the two given tangent vectors as functions of the endpoint conditions.Then we sets up conditions that the functions ought to meet,some of the conditions are predefined function values of some special endpoint conditions,and the predefined function values are obtained from experience data.Lastly the functions are expressed as linear combinations of second or less harmonically related sinusoidal signals,and the coefficients are determined from the preset conditions and function values.The calculation is simple and the end tangent lengths are in (0.5,2.9).Our method is compared with other two methods,and the example curves have satisfactory shapes.