The library QIBSH++ is a C++ object oriented library for the solution of Quasi Interpolation problems. The library is based on a Hermite Quasi Interpolating operator, which was derived as continuous extensions of linear multistep methods applied for the numerical solution of Boundary Value Problems for Ordinary Differential Equations. The library includes the possibility to use Hermite data or to apply a finite difference scheme for derivative approximations, when derivative values are not directly available. The generalization of the quasi interpolation procedure to surfaces and volumes approximation by means of a tensor product technique is also implemented. The method has been also generalized for one dimensional vectorial data, periodic data, and for two dimensional data in cylindrical coordinates, periodic with respect to the angular argument. Numerical tests show that the library could be used efficiently in many practical problems.