Context. Studies of periodic and quasi-periodic phenomena in optical and radio bands are important for understanding the physical processes in quasars. Investigation of periodic/quasi-periodic behavior of the relativistic jets in blazars is particularly significant because it can provide unique information about the formation, collimation, and acceleration of the jets and the properties of the central engines (black hole/accretion disk systems) in blazars. Aims. We investigate the parsec-scale kinematics of the 31 superluminal components observed in blazar 3C279 and attempt to search for evidence of its jet precession and double-jet structure. Methods. The previously suggested precessing jet nozzle model is applied to model-fit the kinematics of its superluminal components observed during the 1981–2015 period. It is shown that the parsec-scale kinematics of the entire source can be interpreted in terms of a double-jet scenario. Results. The superluminal components observed in 3C279 can be divided into two groups that are ejected from two relativistic jets. The two jets have different orientations in space and jet-cone shapes, but both jets precess with the same precession period of 25 yr (16.3 yr in the source frame). The kinematic features of all the superluminal knots (trajectory, core separation, and apparent velocity) can be consistently explained. Their innermost trajectories follow the respective precessing common parabolic patterns with trajectory curvatures that occurred in the outer jet regions at different core separations. The bulk Lorentz factor, Doppler factor, and viewing angle of their motion are derived. The unusual jet-direction change of ∼100° observed in 2010–2011 can be naturally explained. Conclusions. We propose a double-jet structure scenario for 3C279 and suggest that there may be a supermassive black hole binary in the center of 3C279 ejecting two precessing relativistic jets, resulting in its very complex structure and kinematics on parsec scales, and with extremely variable emission across the electromagnetic spectrum. Because the two jets have the same precession period, the precession of the double jet may have originated from the modulation of their jet orientation by the change in their orbital velocity direction relative to the observer. In this case the mass ratio m/M of the binary is approximately equal to the ratio of the jet cone widths, being on the order of ∼0.5.