Realistic Hand manipulation is a key component of immersive virtual reality (VR), yet existing methods often rely on kinematic approach or motion-capture datasets that omit crucial physical attributes such as contact forces and finger torques. Consequently, these approaches prioritize tight, one-size-fits-all grips rather than reflecting users' intended force levels. We present ForceGrip, a deep learning agent that synthesizes realistic hand manipulation motions, faithfully reflecting the user's grip force intention. Instead of mimicking predefined motion datasets, ForceGrip uses generated training scenarios-randomizing object shapes, wrist movements, and trigger input flows-to challenge the agent with a broad spectrum of physical interactions. To effectively learn from these complex tasks, we employ a three-phase curriculum learning framework comprising Finger Positioning, Intention Adaptation, and Dynamic Stabilization. This progressive strategy ensures stable hand-object contact, adaptive force control based on user inputs, and robust handling under dynamic conditions. Additionally, a proximity reward function enhances natural finger motions and accelerates training convergence. Quantitative and qualitative evaluations reveal ForceGrip's superior force controllability and plausibility compared to state-of-the-art methods. Demo videos are available as supplementary material and the code is provided at https://han-dongheun.github.io/ForceGrip.