The precise control and deep understanding of quantum interference in carbon nanotube (CNT) devices are particularly crucial not only for exploring quantum coherent phenomena in clean one-dimensional electronic systems, but also for developing carbon-based nanoelectronics or quantum devices. Here, we construct a double split-gate structure to explore the Aharonov-Bohm (AB) interference effect in individual single-wall CNT p-n junction devices. For the first time, we achieve the AB modulation of conductance with coaxial magnetic fields as low as 3 T, where the flux through the tube is much smaller than the flux quantum. We further demonstrate direct electric-field control of the nonmonotonic magnetoconductance through a gate-tunable built-in electric field, which can be quantitatively understood in combination with the AB phase effect and Landau-Zener tunneling in a CNT p-n junction. Moreover, the nonmonotonic magnetoconductance behavior can be strongly enhanced in the presence of Fabry-Pérot resonances. Our Letter paves the way for exploring and manipulating quantum interference effects with combining magnetic and electric field controls.