We present an electron spin resonance (ESR) study of a single-crystalline spin chain system CuSe2O5 in the frequency range between 9 and 430 GHz. In a wide temperature range above the Neel temperature T-N = 17 K we observe a strong and anisotropic frequency dependence of a resonance linewidth. Although a sizable interchain interaction J(IC) approximate to 0.1J (J is the intrachain interaction) is present in this system, the ESR results agree well with the Oshikawa-Affleck theory for a one-dimensional S = 1/2 Heisenberg antiferromagnet. This theory is used to extract the anisotropies present in CuSe2O5. We find that the symmetric anisotropic exchange J(c) = (0.04 +/- 0.01)J and the antisymmetric Dzyaloshinskii-Moriya (DM) interaction D = (0.05 +/- 0.01)J are very similar in size in this system. Staggered field susceptibility induced by the presence of the DM interaction is witnessed in the macroscopic susceptibility anisotropy.