Efficient　task　scheduling　is　required　to　attain　high　performance　in　both　homogeneous　and　heterogeneous　computing　systems.　An　application　can　be　considered　as　a　task　grid　represented　using　a　Directed　Acyclic　Graph　(DAG).　Solving　such　DAG　representing　a　scheduling　problem　is　an　NP-complete　task.　The　primary　concern　in　this　problem　domain　is　to　reduce　the　schedule　length　with　minimum　complexity.　This　work　presents　a　Hybrid　List-based　Task　Scheduling　using　Duplication　Scheme　(HLTSD)　algorithm　for　heterogeneous　processors.　The　proposed　HLTSD　algorithm　has　the　same　time　complexity　as　that　of　the　recent　state-of-the-art　algorithms.　However,　it　produces　a　minimum　cost　schedule　in　comparison　with　other　related　methods.　This　work　also　presents　a　mathematical　formulation　to　find　task　priorities.　The　processor　selection　phase　is　improved　by　utilizing　the　techniques,　like　entry　task　duplication,　insertion-based　policy,　duplication　of　parent　task　on　other　levels,　and　balancing　the　load　on　each　processor.　The　current　proposal　minimizes　the　overall　makespan　of　execution　by　reasonable　levels.　Performance　of　the　proposed　algorithm　is　evaluated　using　DAGs　adopted　from　various　state-of-the-art　algorithms,　real-world　problems,　like　Gaussian　elimination　(GE)　and　fast　Fourier　transformation　(FFT)　task　graph　and　randomly　generated　graphs　with　diverse　characteristics.　The　proposed　scheme　is　compared　with　four　state-of-the-art　list-based　scheduling　algorithms,　namely　Heterogeneous　Earliest　Finish　Time　(HEFT),　Predict　Earliest　Finish　Time　(PEFT),　Heterogeneous　Scheduling　with　Improved　task　Priority　(HSIP),　and　Task　Scheduling　for　Heterogeneous　Computing　Systems　(TSHCS).　Based　on　the　best　quality　schedule,　the　obtained　results　suggest　that　HLTSD　has　better　results　in　87%　cases.