This paper establishes an air-standard irreversible Dual-Miller cycle (DMC) model with the specific heat ratio (SHR) of working fluid (WF) linearly varying with its temperature. Because the specific heat (SH) of WF varies with combustion reaction in actual internal combustion engine (ICE), the SHR of WF should be a function of temperature but not a constant. In order to accurately reflect the practical characteristics of DMC engine, performance of DMC with linearly variable SHR, and with heat transfer (HT) loss, friction loss (FL) and other internal irreversible losses (IlLs) is analyzed and optimized by applying finite-time thermodynamics. Analytical formulae of the power output (P), efficiency (eta), entropy generation rate (EGR) and ecological function (E) are derived. Relationships among P, eta, E and compression ratio are obtained via numerical calculations. Effects of the design parameters, cycle temperatures and linearly variable SHR of WF on P, eta and E are investigated. Performance differences among the DMC and its simplified cycles, including Otto cycle (OC), Dual cycle (DDC) and Miller cycle (OMC) are compared. Performance characteristics of the DMC with different optimization objective functions (OOFs) are analyzed. The results indicate that the maximum power output (MP), maximum efficiency (MEF) and maximum ecological function (ME) of the DMC are superior to those of OC, DDC and OMC, and optimizing E is the best compromise between optimizing P and optimizing;I. The presented results may be helpful to optimize the performance of practical DMC engines. (C) 2018 Elsevier Ltd. All rights reserved.