The (Ca,R)FeAs2 (R=La,Pr and etc.) superconductors with a signature of superconductivity transition above 40 K possess a new kind of block layers that consist of zig-zag As chains. In this paper, we report the electronic structure of the new (Ca,La)FeAs2 superconductor investigated by both band structure calculations and high resolution angle-resolved photoemission spectroscopy measurements. Band structure calculations indicate that there are four hole-like bands around the zone center $Gamma$(0,0) and two electron-like bands near the zone corner M(pi,pi) in CaFeAs2. In our angle-resolved photoemission measurements on (Ca0.9La0.1})FeAs2, we have observed three hole-like bands around the Gamma point and one electron-like Fermi surface near the M(pi,pi) point. These results provide important information to compare and contrast with the electronic structure of other iron-based compounds in understanding the superconductivity mechanism in the iron-based superconductors.