We can easily learn and perform a variety of movements that fundamentally require complex neuromuscular control. Many empirical findings have demonstrated that a wide range of complex muscle activation patterns could be well captured by the combination of a few functional modules, the so-called muscle synergies. Modularity represented by muscle synergies would simplify the control of a redundant neuromuscular system. However, how the reduction of neuromuscular redundancy through a modular controller contributes to sensorimotor learning remains unclear. To clarify such roles, we constructed a simple neural network model of the motor control system that included three intermediate layers representing neurons in the primary motor cortex, spinal interneurons organized into modules and motoneurons controlling upper-arm muscles. After a model learning period to generate the desired shoulder and/or elbow joint torques, we compared the adaptation to a novel rotational perturbation between modular and non-modular models. A series of simulations demonstrated that the modules reduced the effect of the bias in the distribution of muscle pulling directions, as well as in the distribution of torques associated with individual cortical neurons, which led to a more rapid adaptation to multi-directional force generation. These results suggest that modularity is crucial not only for reducing musculoskeletal redundancy but also for overcoming mechanical bias due to the musculoskeletal geometry allowing for faster adaptation to certain external environments.