In this paper, we present the first complete photometric light curves in the B, V, and R passbands of the neglected contact binary LP Com. Based on the Wilson-Devinney code, it has been found that the LP Com is a W-type W UMa binary with a mass ratio of q=m(2)/m(1)=4.36 and a contact degree of f = 21.3+/-0.3%. By using our new times of minimum light together with those collected from the literature, we found that the observed calculated (O-C) curve shows an upward parabolic variation that corresponds to a long-term increase in the orbital period at a rate of dP/dt = + 2.59 x 10(-7) days yr(-1). Such a long-term increase in its orbital period may be caused by a mass transfer from the less massive component to the more massive one. This indicates that LP Com is in the thermal relaxation oscillation controlled evolution stage. The presence of two dark spots on both companions was used to fit the asymmetry of the light curves. When the upward parabolic change was subtracted, the (O-C)(2) curve reveals a cyclic variation with a period of 10.09 yr and a small amplitude of 0.0028 days. The cyclic variation was investigated by the light-time effect due to the presence of an extremely cool stellar companion.