TOMBO: all-electron mixed-basis approach to condensed matter physics. TOMBO is a computer code for calculating the electronic structure of systems that consist both of core and valence electrons and nuclei, based on density-functional theory. It is based on an all-electron mixed-basis approach, in which the Kohn-Sham (KS) wave function is expressed by a linear combination of plane-waves and atomic-orbitals. This approach can describe both spatially localized and extended orbitals, which enables us to perform all-electron calculations with high accuracy from isolated clusters to periodic crystals. The present paper describes a theory of the all-electron mixed-basis approach, as well as input variables and benchmark tests in TOMBO. The algorithm for accelerating the computational time that is needed to solve the KS equation is also presented.