We have carried out a study of the interstellar medium (ISM) toward a shell-like supernova remnant SNR Puppis A by using the NANTEN CO and ATCA Hi data. We synthesized a comprehensive picture of the SNR radiation by combining the ISM data with the gamma-ray and X-ray distributions. The ISM, both atomic and molecular gas, is dense and highly clumpy, and is distributed along the northeastern edge of the SNR shell. The CO distribution revealed an enhanced line intensity ratio of CO(J = 2-1)/(J = 1-0) transitions as well as CO line broadening, which indicate shock heating/acceleration. The results support that Puppis A is located at 1.4 kpc. The ISM interacting with the SNR has large mass of ∼10 4 M which is dominated by Hi, showing good spatial correspondence with the Fermi-LAT gamma-ray image. This favors the hadronic origin of the gamma-rays, while additional contribution of the leptonic component is not excluded. The distribution of the X-ray ionization timescales within the shell suggests that the shock front ionized various parts of the ISM at epochs ranging over a few to ten 1000 yr. We therefore suggest that the age of the SNR is around 10 4 yr as given by the largest ionization timescale. We estimate the total cosmic ray energy W p to be 10 47 erg, which is well placed in the cosmic-ray escaping phase of an age-W p plot including more than ten SNRs.