  Recent studies have shown that moir\'{e} flat bands in a twisted bilayer
graphene(TBG) can acquire nontrivial Berry curvatures when aligned with
hexagonal boron nitride substrate [1, 2], which can be manifested as a
correlated Chern insulator near the 3/4 filling [3, 4]. In this work, we show
that the large Berry curvatures in the moir\'{e} bands lead to strong nonlinear
Hall(NLH) effect in a strained TBG with general filling factors. Under a weak
uniaxial strain $\sim 0.1\%$, the Berry curvature dipole which characterizes
the nonlinear Hall response can be as large as $\sim$ 200{\AA}, exceeding the
values of all previously known nonlinear Hall materials [5-14] by two orders of
magnitude. The dependence of the giant NLH effect as a function of electric
gating, strain and twist angle is further investigated systematically.
Importantly, we point out that the giant NLH effect appears generically for
twist angle near the magic angle due to the strong susceptibility of nearly
flat moir\'{e} bands to symmetry breaking induced by strains. Our results
establish TBG as a practical platform for tunable NLH effect and novel
transport phenomena driven by nontrivial Berry phases.
