Customer product reviews play a role in improving the quality of products and services for business organizations or their brands. Complaining is an attitude that expresses dissatisfaction with an event or a product not meeting customer expectations. In this paper, we build a Vietnamese Open-domain Complaint Detection dataset (UIT-ViOCD), including 5,485 human-annotated reviews on four categories about product reviews on e-commerce sites. After the data collection phase, we proceed to the annotation task and achieve the inter-annotator agreement (A_m) of 87%. Then, we present an extensive methodology for the research purposes and achieve 92.16% by F1-score for identifying complaints. With the results, in future, we aim to build a system for open-domain complaint detection on E-commerce websites.