In this study, new photometric observations of shallow contact binary CN Andromedae (CN And) were performed and multi-color (BV R) CCD light curves (LCs) were obtained. Simultaneous analysis of new LCs and published radial velocity (RV) data reveals that the system is an early contact binary in which both components have recently filled their inner Roche lobes. Asymmetric LCs were modeled by a dark spot on the primary component and a hot spot on the secondary component that probably resulted from magnetic activity and mass transfer, respectively. Modeling of LCs and RV data allows us to estimate the following absolute parameters: M-1= 1.40 +/- 0.02 M-circle dot, M-2 = 0.55 +/- 0.01 M-circle dot, R-1 = 1.45 +/- 0.02 R-circle dot and R-2 = 0.94 +/- 0.02 R-circle dot. A decreasing orbital period with a rate of dP/dt = -1.5 x 10(-7) d yr(-1) can be seen as evidence that the system is evolving into a contact binary with higher contact degree. Cyclic oscillation of the O - C data was interpreted by the Applegate mechanism and light-time effect due to an unseen component around the close binary system. The hypothetical third component is probably a fully convective red dwarf star with a minimal mass of 0.1 M-circle dot. CN And is at the early phase of the contact stage of its evolution and is an interesting example for studying the formation and evolution of close binaries.