FV CVn is a solar-type (G7) eclipsing binary whose analysis has so far been ignored. We observed it from 2014 January to 2018 May. The first photometric and orbital period investigation are presented here, combined with spectroscopic observations obtained by the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST). The current preliminary solutions show that FV CVn is a new W-subtype contact binary with a mass ratio of q = M-2/M-1 = 2.44(+/- 0.20) and a temperature difference of Delta T = T-2 -T-1 similar or equal to -315 K. The orbital period investigation suggests that a cyclic variation of A = 0.0184(+/- 0.0034) days and P-3 = 17.65(+/- 0.076) years exists in FV CVn. This cyclic variation is analyzed for the light-travel-time effect (LTTE) via the presence of a third body with a minimum mass of M-3min = 0.73(+/- 0.018) M-circle dot, and an orbital semimajor axis shorter than 5.27(+/- 1.62) au. This is in agreement with the presence of a large quantity of a third light in the system. Photometric solutions suggest that the third body contributes about 26.4(+/- 6.3)% in R-c, and 29.0(+/- 5.9)% in I-c to the total light of the multiple system. The additional component may play an important role in the origin and evolution of central close binary. New radial velocities are needed in the future to check the accuracy of the absolute parameters.