The fluctuation of the electron bunch duration due to energy spectrum instability in a laser plasma cathode has been examined. Previous experiments clearly proved that a laser plasma cathode can generate ultrashort electron bunches with a bunch duration of 130fs (FWHM) and a geometrical emittance 0.07πmmmrad. The effect of temporal elongation of electron bunches due to their energy spread is estimated and the results are in good agreement with previous experiments. It is also clarified that the instability of the energy spectrum not only leads to a fluctuation of the bunch shape but also to a time-of-flight jitter, affecting possible future applications of a laser plasma cathode.