The two-neutrino double-β decay matrix elements and half-lives of Ca48 were calculated within a shell-model approach for transitions to the ground state and to the 2+ first excited state of Ti48. We use the full pf model space and the GXPF1A interaction, which was recently proposed to describe the spectroscopic properties of the nuclei in the nuclear mass region A=47-66. Our results are T1/2(0+→0+)=3.3×1019 yr and T1/2(0+→2+)=8. 5×1023 yr. The result for the decay to the Ti48 0+ ground state is in good agreement with experiment. The half-life for the decay to the 2+ state is two orders of magnitude larger than that obtained previously.