Parallel job scheduling has long been an important research issue for high-performance computing (HPC). Most modern parallel application programs can be written with a good property called moldable which allows parallel programs to have the flexibility of exploiting different parallelisms for execution. Some previous research has developed adaptive processor allocation methods for moldable jobs to improve the overall performance of HPC systems. Recently, the concept of HPC as a Service (HPCaaS) was proposed to bring the traditional HPC field into the era of cloud computing. For HPCaaS systems, scheduling jobs with deadline efficiently becomes a crucial issue. This paper explores the issues of scheduling moldable jobs with deadline, which has not received enough research attention yet. We propose and evaluate three possible dynamic scheduling approaches for online moldable jobs with deadline.