We report on a precision measurement of gravitational acceleration using ultracold strontium atoms confined in an amplitude-modulated vertical optical lattice. An uncertainty Δg/g ≈ 10(-7) is reached by measuring at the 5th harmonic of the Bloch frequency. The value obtained with this microscopic quantum system is consistent with the one measured with a classical gravimeter. Using lattice modulation to prepare the atomic sample, we also achieve high visibility of Bloch oscillations for ∼ 20 s. These results can be of relevance for testing gravitational redshift and Newtonian law at micrometer scale.