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 δ Scuti-type pulsating star rather than an EW-type eclipsing binary. On the diagram, J213934 lies inside the classical Cepheid instability strip where most δ Scuti stars are located. The results of pulsating frequency analysis show the fundamental frequency f0 = 6.8195 day−1, the first overtone f1 = 8.8709 day−1 and 4 harmonics or linear combinations. The mass of J213934 is estimated as. 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. [ABSTRACT FROM AUTHOR]