Constructing online High-Definition (HD) maps is crucial for the static environment perception of autonomous driving systems (ADS). Existing solutions typically attempt to detect vectorized HD map elements with unified models; however, these methods often overlook the distinct characteristics of different non-cubic map elements, making accurate distinction challenging. To address these issues, we introduce an expert-based online HD map method, termed MapExpert. MapExpert utilizes sparse experts, distributed by our routers, to describe various non-cubic map elements accurately. Additionally, we propose an auxiliary balance loss function to distribute the load evenly across experts. Furthermore, we theoretically analyze the limitations of prevalent bird's-eye view (BEV) feature temporal fusion methods and introduce an efficient temporal fusion module called Learnable Weighted Moving Descentage. This module effectively integrates relevant historical information into the final BEV features. Combined with an enhanced slice head branch, the proposed MapExpert achieves state-of-the-art performance and maintains good efficiency on both nuScenes and Argoverse2 datasets.