The authors substantiate a method for constructing a local quasigeoid height model based on given anomaly values at discrete points along the axis of a linear object route. It is based on approximating the differences between EGM-2008 height anomalies and the quasigeoid using piecewise algebraic polynomials with conditions of continuity and smoothness at their junctions. The necessary formulas for calculating the model parameters and assessing its accuracy are presented. Experimental studies of the local quasigeoid model constructed for a section of the M-11 high-speed motorway route are presented, they confirmed the effectiveness of the proposed approach. The constructed second-order model allows transforming geodetic heights obtained by GNSS into normal ones of the Baltic Height System 1977 with a root-mean-square error of about 10 mm on this route section. The results of the work are of practical importance for improving the accuracy of engineering and geodetic surveys of linear objects performed using satellite methods of space geodesy