•An innovative strategy for recycling waste concrete is proposed.•Mass ratio of total waste content in recycled lump/aggregate concrete is great.•Good strength can still be attained when mass ratio of total waste content is 55%.•Formula is proposed to predict elastic modulus of recycled lump/aggregate concrete.•Recycled aggragate concrete with 100% replacement ratio is not suggested to be used. Reusing coarsely crushed demolished concrete lumps (DCLs) and recycled coarse aggregates (RAs) simultaneously is proposed as a way to improve the total waste content in concrete. The compressive behaviour of compound concrete containing DCLs and recycled aggregate concrete (RAC), which referred to as recycled lump/aggregate concrete (RLAC), was experimentally investigated. In addition, mercury intrusion porosimetry and scanning electron microscope were employed to investigate the interfacial transition zone between DCLs and RAC at the micro level. The results revealed that: (a) the total waste content in RLAC can reach more than twice that in RAC in engineering practice; (b) when the compressive strength of RAC stays almost unchanged, only the compressive strength of RLAC containing RAC with 100% RA replacement ratio is relatively much lower; (c) satisfactory compressive strength can still be attained even when the total waste content in RLAC reaches 54.6%; and (d) when the RA replacement ratio is 100%, the porosity and harmful pores in the fresh mortar surrounding DCLs increase remarkably.