Fourier ptychography (FP) is a newly developed imaging technology, which can reconstruct high-resolution (HR) wide-field image from a series of low-resolution (LR) images. The limitation of FP is its long acquisition and reconstruction time due to the numerous LR images that are needed and the low illumination intensity of light-emitting diodes (LEDs) which lead to long exposure time of imaging sensors. Many researches have been done to speed up FP. The available speeding-up methods with single LED illumination are still constrained by low illumination intensity of LED. Although multi-illumination methods can improve illumination intensity, they are time-consuming during spectrum decomposition. In this paper, we demonstrate a new efficient method, termed symmetric Fourier ptychography (SFP). For thin samples irrespective of phases, two center-symmetric illuminations generate the same intensity distribution, so that two center-symmetric LEDs used in FP can be lit up simultaneously and the illumination intensity is doubled. Spectra have central conjugate symmetry in Fourier domain so that only half of spectra need recovering, then, the processing time can be reduced by about 50%. Simulations are conducted with the Cameraman image as input amplitude. The LR images are generated based on the FP simulation process and then the LR images generated by LEDs from two center-symmetrical positions are summed. Furthermore, HR images are recovered by using FP reconstruction algorithms. It is found that root-mean-square-error of SFP is almost the same as that of traditional FP, which indicates that the SFP can achieve the same performance as that of traditional FP. Then, central conjugate symmetry is adopted in Fourier domain, where only half of spectra are recovered and the other half of spectra are obtained from conjugate symmetry. It proves that HR images can be recovered based on central conjugate symmetry in Fourier domain and 50% of processing time is saved. For imaging experiments of USAF target and biological samples, two LEDs of central symmetry are lit up simultaneously, and 113 LR images are gathered in contrast with 225 ones of traditional FP. It is also found that SFP can achieve the same resolution as that of the traditional FP. In the meantime, SFP can reduce about 50% LR images and save about 70% acquisition time without increasing the complexity of FP system and algorithms. In addition, SFP can be combined with other methods to further speed up the speed of FP, and its feasibility is proven by the experimental results of combination with adaptive Fourier ptychography. All results in this paper indicate that the proposed method has the potential to improve the application of FP in real-time imaging.