Existing Android malware detection systems primarily concentrate on detecting malware apps, leaving a gap in the research concerning the detection of malicious components in apps. In this work, we propose a novel approach to detect fine-granularity malicious components for Android apps and build a prototype (AMCDroid). For a given app, AMCDroid first models app behavior to a homogenous graph based on the call graph and code statements of the app. Then, the graph is converted to a statement tree sequence for malware detection through the AST-based Neural Network with Feature Mapping (ASTNNF) model. Finally, if the app is detected as malware, AMCDroid applies fine-granularity malicious component detection (MCD) algorithm which is based on many-objective genetic algorithm to the homogenous graph for detecting malicious component in the app adaptively. We evaluate AMCDroid on 95,134 samples. Compared with the other two state-of-the-art methods in malware detection, AMCDroid gets the highest performance on the test set with 0.9699 F1-Score, and shows better robustness in facing obfuscation. Moreover, AMCDroid is capable of detecting fine-granularity malicious components of (obfuscated) malware apps. Especially, its average F1-Score exceeds another state-of-the-art method by 50%.