We present a theoretical study of electron transport properties through experimentally controllable graphene nanobubbles [P. Jia et al., Nat. Commun. 10 (2019) 1] employing a tight-binding model and the non-equilibrium Green's function formalism. Sharp conductance peaks are observed at low energy region which signifies the emergence of quasi-bound states caused by pseudomagnetic field in the strained nanobubbles. Analysis based on local density of states reveals the nature of electron transmission at peak energies. Our results also show that the emergence of quasi-bound states and its role in electron transport depend on both strain strength and bubble size: when the strain or size of the bubble increases, more quasi-bound states emerge and resonant tunnelling assisted by these quasi-bound states becomes dominant.