ZZ Cassiopeiae (ZZ Cas) is an early spectral B-type close binary with an orbital period of 1.243527 d. By analyzing the continuous light curve obtained by TESS, and the spectroscopic data with low resolution observed by the 2.16 m telescope in Xinglong station, we found that it is a semi-detached binary; the secondary component fulfills the critical Roche lobe, while the more massive one is detached from the lobes with a fraction of the third light 1.82%. Our O-C diagram time spanning 32.6 yr shows a cyclical oscillation with a semi-amplitude of 0.0255(+/- 0.0010) d and a period of 19.11(+/- 0.27) yr superimposed on an upward parabolic curve with a period increase rate of dP/dt = +2.93 x 10(-8) d yr(-1). The upward parabolic variation and photometric solutions reveal that ZZ Cas is undergoing a late Case A mass transfer process on the nuclear timescale of the secondary component, and it was formed from originally detached binary systems. Its evolution is different from that of V606 Cen in the massive binaries. Meanwhile, the cyclic change in the O-C curve can be interpreted by the light-travel-time effect via the presence of a tertiary body. The tertiary companion with a minimal mass of M-3 = 4.23(+/- 0.22) M-circle dot orbits around the central eclipsing binary in an eccentric orbit (e = 0.62). The estimation of an extremely low luminosity ratio of the primary component and the tertiary body may reveal that the additional component is a low-mass triple system or a compact object candidate.