It is shown in the limit-circle case that system of root functions of the non-self-adjoint maximal dissipative (accumulative) Bessel operator and its perturbation Sturm-Liouville operator form a complete system in the Hilbert space. Furthermore, asymptotic behavior of the eigenvalues of the maximal dissipative (accumulative) Bessel operators is investigated, and it is proved that system of root functions form a basis (Riesz and Bari bases) in the same Hilbert space. Copyright (c) 2014 John Wiley & Sons, Ltd.