  Binary millisecond pulsars (MSPs) are believed to have descended from
low-mass X-ray binaries (LMXBs), which have experienced substantial mass
transfer and tidal circularization. Therefore, they should have very circular
orbits. However, the discovery of several eccentric binary MSPs (with
eccentricity $e\sim 0.01-0.1$) challenges this standard picture. Three models
have been proposed thus far based on accretion-induced collapse of massive
white dwarfs (WDs), neutron star-strange star transition, and formation of
circumbinary disks. All of them are subject to various uncertainties, and are
not entirely consistent with observations. Here we propose an alternative model
taking into account the influence of thermonuclear flashes on proto-WDs. We
assume that the flashes lead to asymmetrical mass ejection, which imparts a
mild kick on the proto-WDs. By simulating orbital changes of binary MSPs with
multiple shell flashes, we show that it is possible to reproduce the observed
eccentricities, provided that the kick velocities are around a few kms$^{-1}$.
