Based on the approach within the single-electron approximation (SEA) frame, we numerically solve the two-dimensional (2D) time-dependent Schr
o
¨
dinger equation of N2 molecules under co-rotating and counter-rotating circularly polarized attosecond pulses. The vortex structure appears in counter-rotating circularly laser fields rather than the co-rotating case. The calculated vortex structures corresponding to the photoionization are found to be sensitive to the time delays T
d
of the two pulses, laser ellipticities and carrier envelope phases (CEPs). As the ellipticity increases to 1, the momentum distribution rotates and a vortex structure appears, and the interference is proved to play an important role in momentum distribution. The vortex structures also rotate clockwisely as the relative CEPs increase. The arms of the vortex structure become longer and thinner with the increasing T
d
. All these phenomena can be well understood by the attosecond perturbation ionization theory and the interference effect. Our findings clarify the applicability of the SEA model of diatomic molecules in attosecond extreme-ultraviolet fields.