Workflow scheduling is one of the most challenging problems in cloud computing. This paper proposes a heuristic algorithm task type first algorithm (T2FA) for solving deadline-constrained workflow scheduling in cloud with multicore resource (DWS_CMR). The objectives to be minimized are the maximal completion time (i.e., makespan) and the total costs. Firstly, resource model and workflow application model are introduced. Resource model has the configurations of multicore, processing capacity, bandwidth and leasing price, and workflow application model is described by directed acyclic graph (DAG). Based on above models, the mathematical model of DWS-CMR is established, which allows multiple tasks to run concurrently on multicore resources. Secondly, to exploit the characteristics of the problem, the structures of DAG are decomposed and formulated. Merging tasks conforming to the first structure into task blocks can simplify DAG. Four special types of tasks are extracted from the second and third structures, and are preferentially scheduled in task scheduling stage. Then, a new interrelated calculation method of estimated start time and actual start time of tasks is proposed, which can complete the task-To-resource mapping. Finally, T2FA is devised, which incorporates two important phases, including pre-processing and task scheduling. Experimental results show that T2FA can achieve significantly better schedules in most test cases compared to several existing algorithms.