Recently, cloud computing has emerged as a realization of utility computing in which users have to pay for the utilized resources. Besides, there is a growing request for automation of current scientific and business applications in the form of workflows in cloud environments. While users wish to pay as less monetary cost as possible for executing their workflows, the time-constrained nature of this type of applications is a barrier to cost minimization. Solving this problem requires developing new efficient and customized scheduling algorithms. To this end, in this paper, first we have formulated a cloud-customized task-resource mapping which is exploited as the cost function of our Genetic Algorithm (GA)-based scheduling method. Also, by using indirect chromosome representation scheme and proposing a novel genotype-to-phenotype mapping (GPM), the algorithm guarantees the feasibility of the solutions and removes the restrictions imposed by evolutional operators and overheads of repair phases. Moreover, a key property of our method, called neutrality, strongly improves the quality of the solutions and the convergence rate. The results of experiments done on some real-world workflow benchmarks show that monetary cost of the solutions found by our algorithm outperform those of some recently successful scheduling algorithms. Moreover, the run time needed for the proposed method to produce solutions is in the order of seconds which demonstrates its quickness compared to other mentioned algorithms.