The magnetic field dependence of the spin-lattice relaxation rate 1/T1 of 119Sn in CeNiSn has been measured down to 20 mK in a field range of 0.2-8 T. (T1T)-1 is constant below 1 K, which depends on the external field in such a manner that its value stays constant to 2 T, while it increases linearly with the field up to 8 T. It is shown that this magnetic field dependence of (T1T)-1 is well explained by the simple scenario that the quasiparticle density of states at the Fermi level is produced by the Zeeman splitting of the up- and down-spin bands, keeping its V-shaped gapped structure unchanged for fields less than 8 T. The present experiment has elucidated that CeNiSn is in a semimetallic ground state with a low carrier density and the application of a magnetic field exceeding 2 T turns out to supply effective carriers.