The proposed heavy ion inertial fusion (HIF) scenarios require ampere class low charge state ion beams of heavy species. The laser ion source (LIS) is recognized as one of the promising candidates of ion beam providers, since it can deliver high brightness heavy ion beams to accelerators. The design of LIS for the HIF depends on the accelerator structure and accelerator complex following the source. In this article, we discuss the specifications and design of an appropriate LIS assuming two major types of the accelerators: radio frequency (RF) high quality factor cavity type and non-resonant induction core type. We believe that a properly designed LIS would satisfy the requirements of both types, while some issues need to be verified experimentally.