A novel transcritical cascade-Organic Rankine Cycle (C-ORC) system was proposed to recover multi-grade waste heat from a typical heavy-duty diesel engine. The C-ORC comprises of a high-temperature ORC loop (HT-Loop) and a low temperature ORC loop (LT-Loop) to recover waste heat from an engine's exhaust gas (EG), exhaust gas recirculation (EGR), jacket water (JW) and charge air (CA) in a cascaded pattern. In order to reveal the full performance of the C-ORC system, with due consideration to diesel's complex practical running conditions, multi-approach evaluations were conducted containing two parts: Part A - thermodynamic evaluations of the energy and exergy aspects and Part B - techno-economic evaluations on costs and benefits aspects. This paper shows the Part A-evaluations of the C-ORC, focusing on indexes including recovered waste heat, net power output, thermal efficiencies and exergy efficiencies. First of all, distributions of the engine's multi-grade waste heat were studied to reveal the characteristics and utilization potential of waste energy. The comparison and screening of working fluids were carried out next to find the best fluids - for the HT-Loop and LT-Loop respectively based on the rated engine condition. Toluene, decane, cyclohexane and D4 were four proper alternatives for the HT-Loop while R143a, R125, R218 and R41 were four proper alternatives for the LT-Loop. Comparisons indicated that toluene and R143a made the perfect match for the C-ORC with the highest net power output (33.9 kW), thermal efficiency (9.9%) and exergy efficiency (39.1%). The rankings of the two groups of alternate fluids based on their thermodynamic performance were: toluene > decane > cyclohexane > D4 and R143a > R125 > R218 > R41. Finally, the C-ORC's performance was evaluated based on the engine's practical operating conditions. Results indicated that, the engine's waste heat was only able to drive the C-ORC system when the engine torque was higher than 917 N m. The maximal recovered heat of the EG, EGR, CA and JW were 153.0 kW, 9.1 kW, 37.5 kW and 267.0 kW under available conditions; the highest net power output, thermal efficiency and exergy efficiency were 38.2 kW, 11.3%, 38.7% respectively; and the largest efficiency increment to the original engine was up to 16.0%. Summarily, thermodynamic evaluations from Part A-reveal that the proposed C-ORC has significant heat-recovery capacities and efficiency-promotion potential. (C) 2015 Elsevier Ltd. All rights reserved.