Orbital-period variations of the neglected W UMa-type binary star, NY Lyr, were analyzed based on two newly determined eclipse times together with the others compiled from the literature. A cyclic oscillation with a period of 82.1 yr and an amplitude of 0.0247 d was discovered to be superimposed on a continuous period increase (dP/dt = +1.33 × 10−7 d yr−1). After the long-term period increase and the large-amplitude cyclic oscillation were removed from the O–C diagram, the residuals suggest that there is another small-amplitude period oscillation (A 4 = 0.0053 d, P 4 = 19.4 years) in the orbital period changes. As in the cases of AH Cnc and AD Cnc, both the continuous period increase and the two cyclic period oscillations make NY Lyr an interesting system to study in the future. In order to understand the evolutionary state of the binary system, new photometric and spectroscopic observations and a careful investigation on those data are needed.