Recently, multivariate temporal data classification has been widely applied on many fields, such as bio-signals analysis, stocks prediction and weather forecasting. Multivariate temporal data contains hybrid type of attributes like numeric and categorical ones. However, most classification methods proposed in the past researches are not directly applicable to the multivariate temporal data with multiple types. Additionally, no useful and readable rules are provided in the existing methods for advanced classification analysis. In this paper, we proposed a novel algorithm named Progressive Temporal Class Rule Miner (PTCR-Miner) for classification on multivariate temporal data with a rule-based design. Through our algorithm, the classification rules discovered follow the purification concept we defined to be comprehensible and intuitive for general users to use on data classification. A series of experiments were conducted to evaluate our method with a multivariate temporal data simulator. The experimental results showed that PTCR-Miner performs effectively and efficiently on different simulated multivariate temporal datasets. Additionally, a real dataset related to asthma monitoring was also tested and the results showed that our classification mechanism works stably for asthma attack predictions. This means the discovered rules are really helpful and comprehensible for data classification. Furthermore, the rule-based and flexible architecture make PTCR-Miner more applicable to different application areas of multivariate temporal data classification.