Particle-in-cell (PIC) simulation results of sustained acceleration of electron-positron (e+e-) plasmas by comoving electromagnetic (EM) pulses are presented.When a thin slab of overdense e+e-plasma is irradiated with linear-polarized ultra-intense short laser pulses from both sides, the pulses are transmitted when the plasma is compressed to thinner than ~ 2 relativistic skin depths. A fraction of the plasma is then captured and efficiently accelerated by self-induced JxB forces. For 1µm laser and10 21 Wcm -2 intensity, the maximum energy exceedsGeV in a picosecond.Recent advances in ultra-intense short-pulse lasers (ULs) [1,2] revolutionize particle acceleration via intense electromagnetic (EM) fields [3]. Most proposed laser acceleration schemes (e.g. laser wakefield accelerator (LWFA), plasma wakefield accelerator (PWFA) [4], free-wave accelerator (FWA) [5]) require propagating lasers in an underdense plasma (ω pe =(4πne 2 /m) 1/2 <ω o =2πc/λ, λ=laser wavelength, n=electron density, m=electron mass). In such schemes the energy gain/distance [4] and particle beam intensity are constrained by the underdense requirement. Here we report particle-in-cell (PIC) simulation results of a radically different concept: comoving acceleration of overdense (ω pe >ω o ) plasmas using colliding ULpulses. This colliding laser pulses accelerator (CLPA) has properties, such as higher acceleration gradient and particle beam intensity, that are complementary to underdense schemes.When an intense EM pulse with Ω e (=eB o /mc=a o ω o , a o =normalized vector potential)>ω pe initially imbedded in an overdense plasma tries to escape, it induces a skin current J that inhibits the EM field from leaving. The induced J x B (ponderomotive) force then accelerates the surface plasma to follow the EM pulse. As the EM pulse "pulls" the surface plasma, it is slowed by plasma loading (group velocity < c), allowing the fastest particles to "comove" with the EM pulse. Since slower particles eventually fall behind, the plasma loading decreases and the EM pulse accelerates over time. A dwindling number of fast particles gets accelerated indefinitely by the comoving EM force, reaching maximum Lorentz factors γ max >a o 2 /2 (ponderomotive limit[6]) >>(Ω e /ω pe ) 2 . This phenomenon, called the diamagnetic relativistic pulse accelerator (DRPA)[7], is a nonlinear relativistic phenomenon, with no analog in the weak field (Ω e /ω pe <1), low density (ω o >ω pe ) regime or test particle limit.But DRPA is difficult to achieve in the laboratory, since vacuum EM waves cannot penetrate an overdense plasma beyond the relativistic skin depth [8]. Fig. 1 shows the PIC simulation of a single UL irradiating an overdense e+e-plasma. All upstream plasma is snowplowed by the UL