Measurements of the magnetization and specific heat have been carried out for Co2TeO3Cl2 with a sawtooth lattice having two crystallographically distinct Co2+ sites. A powder neutron diffraction study has revealed that two magnetic transitions take place at T-N1 similar to 73 K and T-N2 similar to 15 K. Below T-N1, Co spins at the apical sites of the sawtooth lattice order antiferromagnetically with their directions parallel to the b-axis. Co spins at the basal sites order antiferromagnetically at TN2 with their directions canted in the ab-plane from the a-axis by Dzyaloshinski-Moriya interaction. At this transition, no change in the spin structure at the apical sites has been observed. Discussion on possible origins of these complicated spin structure is presented.