To study the effect of different circular groove numbers of bull′s eye structures on the enhanced transmission in terahertz region, two bull′s eye samples were fabricated with five circular grooves and fifteen circular grooves on aluminum slabs, respectively. Transmitted terahertz signals from two bull′s eye samples were obtained by using terahertz time-domain spectroscopy. Experimental results show that for both samples, broad-band terahertz reference signal from 0.1 THz to 2.7 THz was filtered to be narrow-band signal, the center peak was at 0.53 THz, the transmission efficiency can reach 55.7% by five circular grooves and 68.3% by fifteen circular grooves through the center holes respectively. The differences on band widths and amplitudes of transmitted terahertz signals from small sample and big sample with different circular groove numbers come from insufficient periodical extension and leakage from edge of structure. Furthermore, spoof surface plasmon polaritons theory was employed to analyze filter phenomena of transmitted signals from different size bull′s eye structures with the help of finite element method. The simulated results agree well with the experimental results, both proved that the circular groove numbers can affect the enhancemen of the transmission in terahertz region.