We have developed a laser ion source for the target-like fragments (TLFs) produced in multi-nucleon transfer (MNT) reactions. The operation principle of the source is based on the in-gas laser ionization and spectroscopy (IGLIS) approach. In the source TLFs are thermalized and neutralized in high pressure and high purity argon gas, and are extracted after being selectively re-ionized in a multi-step laser resonance ionization process. The laser ion source has been implemented at the KEK Isotope Separation System (KISS) for β-decay spectroscopy of neutron-rich isotopes with N=126 of nuclear astrophysical interest. The simulations of gas flow and ion-beam optics have been performed to optimize the gas cell for efficient thermalization and fast transporting the TLFs, and the mass-separator for efficient transport with high mass-resolving power, respectively. To confirm the performances expected at the design stage, off-line experiments have been performed by using 56Fe atoms evaporated from a filament in the gas cell. The gas-transport time of 230ms in the argon cell and the measured KISS mass-resolving power of 900 are consistent with the designed values. The high purity of the gas-cell system, which is extremely important for efficient and highly-selective production of laser ions, was achieved and confirmed from the mass distribution of the extracted ions. After the off-line tests, on-line experiments were conducted by directly injecting energetic 56Fe beam into the gas cell. After thermalization of the injected 56Fe beam, laser-produced singly-charged 56Fe+ ions were extracted. The extraction efficiency and selectivity of the gas cell in the presence of plasma induced by 56Fe beam injection as well as the time profile of the extracted ions were investigated; extraction efficiency of 0.25%, a beam purity of >99% and an extraction time of 270ms. It has been confirmed that the performance of the KISS laser ion source is satisfactory to start the measurements of lifetimes of the β-decayed nuclei with N=126.