  We report on our 51V-NMR study of static and dynamical magnetic properties in
the quasi-one-dimensional antiferromagnet BaCo2V2O8. Although the NMR spectrum
shows well-defined antiferromagnetic (AF) order in the N\'eel ground state, the
AF characteristic from the NMR spectrum is incomplete between 3.5 K and TN= 5.4
K, which could be affected by quantum spin fluctuations. The AF NMR spectrum
indicates two V sites experiencing different magnetic field magnitudes, HA1=2.1
kOe and HA2=3.8 kOe. These internal fields could be explained by accounting for
the classical and the pseudo-dipolar fields from Co2+ spins with a proposed
magnetic structure based on the neutron diffraction measurements. In the
paramagnetic state, the nuclear spin relaxation is dominated by AF spin
fluctuations through the dipolar-type coupling between V and surrounding Co2+
ions. The linear relation between the nuclear spin-lattice relaxation rate
1/T1T and the magnetic susceptibility chi indicates that the Q component of
magnetic susceptibility chi(Q) is roughly proportional to chi, where Q is the
AF wave number. A change in slope of 1/T1T with respect to \chi around 150 K
suggests a change in the AF spin fluctuation spectrum.
