Call graph construction is the foundation of inter-procedural static analysis. PYCG is the state-of-the-art approach for constructing call graphs for Python programs. Unfortunately, PyCG does not scale to large programs when adapted to whole-program analysis where application and dependent libraries are both analyzed. Moreover, PyCG is flow-insensitive and does not fully support Python's features, hindering its accuracy. To overcome these drawbacks, we propose a scalable and precise approach for constructing application-centered call graphs for Python programs, and implement it as a prototype tool JARVIS. JARVIS maintains a type graph (i.e., type relations of program identifiers) for each function in a program to allow type inference. Taking one function as an input, JARVIS generates the call graph on-the-fly, where flow-sensitive intra-procedural analysis and inter-procedural analysis are conducted in turn and strong updates are conducted. Our evaluation on a micro-benchmark of 135 small Python programs and a macro-benchmark of 6 real-world Python applications has demonstrated that JARVIS can significantly improve PYCG by at least 67% faster in time, 84% higher in precision, and at least 20% higher in recall.