In Ca3Co2O6 with one-dimensional ferromagnetic Co chains, magnetization measurements have been performed under pressure up to 1.40 GPa. From the temperature and magnetic field dependences of magnetization, we revealed the magnetic phase diagram of Ca3Co2O6. As pressure is applied to the sample, the magnetic ordering temperature Tc1 increases linearly at the similar rate in all fields up to 5.0 T. The spin-flip temperature Tflip and the spin-flip field Hflip show the linear pressure dependence. These results indicate that the lattice compression enhances a nearest-neighbor antiferromagnetic interaction J1 between chains. By applying pressure, the ferrimagnetic ordering temperature Tc2 increases in 0.5 T, suggesting the enhancement of a second-nearest-neighbor ferromagnetic interaction J2.