Aiming at the conflict between the makespan and execution cost of cloud workflows with deadlines， a Hybrid Adaptive Particle Swarm Optimization algorithm for workflow scheduling （HAPSO） was proposed. Firstly， a Directed Acyclic Graph （DAG） cloud workflow scheduling model was established based on deadlines. Secondly， through the combination of norm ideal points and adaptive weights， the DAG scheduling model was transformed into a multi-objective optimization problem that weighs DAG makespan and execution cost. Finally， based on Particle Swarm Optimization （PSO） algorithm， the adaptive inertia weight， the adaptive learning factors， the probability switching mechanism of flower pollination algorithm， Firefly Algorithm （FA） and the particle out-of-bound processing method were added to balance the global search ability and the local search ability of the particle swarm， and then to solve the objective optimization problem of DAG makespan and execution cost. The optimization results of PSO， Weight Particle Swarm Optimization （WPSO）， Ant Colony Optimization （ACO） and HAPSO were compared and analyzed in the experiment. Experimental results show that HAPSO reduces the multi-objective function value by 40.9% to 81.1% that weighs the makespan and execution cost of workflow （30~300 tasks）， and HAPSO effectively weighs the makespan and execution cost with the constraints of workflow deadlines. In addition， HAPSO also has a good effect on the single objective of reducing the makespan or execution cost， which verifies the universality of HAPSO.