This paper presents the novel contact force control approach of a quad-rotor system to interact with the environment in the constrained space. Although the quad-rotor system is not rigid, a contact force in the altitude can be regulated by the position-based impedance force control scheme that adjusts the reference trajectory with respect to the applied force through an admittance filter. This simplifies the force control application. Simulation studies of force tracking control tasks are performed to evaluate the feasibility of the proposed force control schemes.