Chirped laser pulses are investigated theoretically for laser wakefield (LW) and direct laser (DL) acceleration of electrons in the plasma-bubble regime. Chirping of laser pulse with a suitable frequency allows a better trapping of electron in bubble regime which enforces a strong betatron resonance inside the plasma bubble. Linear and non-linear effects of frequency chirp determine electron acceleration, de-phasing, beam quality in terms of energy spread and high energy from the direct laser field and its plasma wake in bubble regime. Gaussian chirped laser pulse exhibit high energy to the electrons compared with linear and other non-linear chirped pulses in plasma-bubble regime. The investigation with chirped laser pulse opens new dimension to hybrid LW-DL acceleration mechanism in bubble regime.