We have performed magnetostriction and ultrasound measurements on the quasi-one-dimensional S = 1/2 Ising-like antiferromagnet BaCo2V2O8 in high magnetic fields of up to 51 T. The magnetostriction shows lattice shrinking along the c-axis, and we interpret it as the lattice distortion caused by exchange striction and Van-Vleck paramagnetism. It is clarified that the field dependence of sound velocity is correlated to the magnetostriction. We observed a pronounced softening in the sound velocity of the longitudinal-acoustic c(33) mode and found a novel phase transition.