We consider E polarized bound states in the radiation continuum (BICs) in circular periodical array of infinitely long N dielectric rods. We find that each true BIC which occurs in the infinite linear array finds its counterpart in the circular array with extremely large quality factor to define them as the near-BICs.We argue that the quality factor of the symmetry near-BICs behave as $e^{\lambda N}$ where $\lambda$ is a material parameter dependent on the radius and refraction index of the rods. We find also numerically the non-symmetry protected near-BICs tuned by the radius of rods. They are localized with exponential accuracy outside the circular array but fill whole inner space of the circular array forming near-BICs with orbital angular momentum.