The conformational and dynamical properties of a tethered semiflexible polymer chain under tangential active force (f_{a}) are studied by using the Langevin dynamics simulation method. The head of the polymer is fixed near an infinite flat surface at z=0. The polymer is equilibrated first at f_{a}=0 and then subjected to the active force. Under the influence of the active force, the polymer is gradually compressed. Specially, for large f_{a} and large bending rigidity (k_{b}), the polymer is buckled into a quasihelical structure rotating around the z axis at the steady state. It is found that both the radius of the quasihelical structure (R) and the angular velocity of the rotation (ω) are nearly independent of the polymer length (N), but show scaling relations with f_{a} and k_{b}, i.e., R∝f_{a}^{-1/3}k_{b}^{1/3} and ω∝f_{a}^{4/3}k_{b}^{-1/3}, which are explained by simple dynamical models. Before reaching the steady state, it is further found that the buckling velocity of the polymer is proportional to f_{a} but roughly independent of k_{b} and N, then the buckling time (t_{b}) can be described by a scaling relation t_{b}∝Nf_{a}^{-1}. The underlying mechanism of the buckling process is revealed.