Muons produced by the Bethe–Heitler process from laser wakefield accelerated electrons interacting with high materials have velocities close to the laser wakefield. It is possible to accelerate those muons with laser wakefield directly. Therefore for the first time we propose an all-optical ‘Generator and Booster’ scheme to accelerate the produced muons by another laser wakefield to supply a prompt, compact, low cost and controllable muon source in laser laboratories. The trapping and acceleration of muons are analyzed by one-dimensional analytic model and verified by two-dimensional particle-in-cell (PIC) simulation. It is shown that muons can be trapped in a broad energy range and accelerated to higher energy than that of electrons for longer dephasing length. We further extrapolate the dependence of the maximum acceleration energy of muons with the laser wakefield relativistic factor and the relevant initial energy . It is shown that a maximum energy up to 15.2 GeV is promising with and on the existing short pulse laser facilities.