Nowadays, robots gradually have more autonomy to operate alongside people not only on assembly lines, but also in daily spaces such as kitchens, museums, or hospitals. In these scenarios, a robot must demonstrate a high degree of adaptability in realtime dynamic situations while satisfying task compliance objectives such as collision avoidance. The robot skill also needs to be programmed with ease to cope with an enormous variety of task behaviors. To achieve this, we propose Task-parameterized Riemannian Motion Policy (TP-RMP) framework to address the challenges associated with learning and reproducing the skills under multiple task objectives and situations. Specifically, the task objectives are viewed as multiple subtasks, learned as stable policies from demonstrations. The learned policies are also task conditioned and able to cope with real-time changing task situations. Under the RMPflow framework, our approach synthesizes a stable global policy in the configuration space that combines the behaviors of these learned subtasks. The resulting global policy is a weighted combination of the learned policies satisfying the robot’s kinematic and environmental constraints. Finally, we demonstrate the benchmarks of TP-RMP under increasing task difficulties in terms of external disturbances and skill extrapolation outside of the demonstration region.