By analyzing the V, R-c, and I-c light curves of the two neglected W U Ma-type binaries EF CVn and EH CVn using the Wilson-Devinney code, we have discovered that EF CVn is a median contact binary while EH CVn is a shallow contact binary, and they are both W-subtype binary systems. The mass ratio and fillout factor of EF CVn are q = 3.493 +/- 0.063 and f = 32.0% +/- 12.9%, respectively. Those of EH CVn are q = 3.331 +/- 0.052 and f= 19.2% +/- 10.9%, respectively. The addition of a dark spot on the secondary star is used to interpret the asymmetric light curves of EF CVn. An orbital period analysis of EF CVn indicates that there is a cyclic oscillation with an amplitude of 0.0064d and a period of 15.65 yr, accompanied by a continuous increase at a rate of dp/dt = 4.52 x 10(-7) d yr(-1). The periodic oscillation can reasonably be explained by the light travel-time effect of an additional component. The secular increase is probably generated by conservative mass transfer from the primary star to the secondary star. Mean-while, an analysis of the orbital period of EH CVn was also performed. A long-term period decrease at a rate of dp/dt= -5.20 x 10(-8) d yr(-1) was discovered; this is possibly interpreted as caused by mass transfer from the more massive component to the less massive component.