The recently observed large Rashba-type spin splitting in the BiTeX(X=I,Br,Cl) bulk states enables observation of the transition in Fermi surface topology from spindle torus to torus with varying the carrier density and offers an ideal platform for achieving practical spintronic applications and realizing nontrivial phenomena such as topological superconductivity and Majorana fermions. Here we use Shubnikov-de Haas oscillations to investigate the electronic structure of the bulk conduction band of BiTeCl single crystals with different carrier densities. We observe the topological transition of the Fermi surface (FS) from a spindle torus to a torus. The Landau-level fan diagram reveals the expected nontrivial π Berry phase for both the inner and outer FSs. Angle-dependent oscillation measurements reveal three-dimensional FS topology when the Fermi level lies in the vicinity of the Dirac point. All the observations are consistent with large Rashba spin-orbit splitting in the bulk conduction band.