CSS J213934.3-050020 (hereafter J213934) was originally found as an EW-type eclipsing binary star with a period of 0.225456 days by Catalina Real-time Transient Survey. With the stellar atmospheric parameters from the LAMOST, it is found that the temperature is much higher than those of normal EW-type binaries and does not follow the period-temperature relation of EW-type eclipsing binary stars. To study the physical properties of the variable star, new B and V light curves were obtained by using the 70 cm telescope at the Lijiang station of Yunnan Observatories. It is detected that this variable star is a high-amplitude delta Scuti-type pulsating star rather than an EW-type eclipsing binary. On the logg-T diagram, J213934 lies inside the classical Cepheid instability strip where most delta Scuti stars are located. The results of pulsating frequency analysis show the fundamental frequency f(0) = 6.8195 day(-1), the first overtone f(1) = 8.8709 day(-1) and 4 harmonics or linear combinations. The mass of J213934 is estimated as 1.83(-0.21)(+0.27)M circle dot. The period is revised as 0.11272960 days by using 16 new determined times of light maximum. Meanwhile, it is discovered that its O - C curve shows an upward parabolic variation and a sinusoidal variation. The upward parabolic variation may be a part of a cyclic change or a long-time pulsation period increase caused by its evolution. The sinusoidal variation may be caused by the light-travel-time effect via the presence of a companion star.