Coarse-grained (CG) models of biomolecules have recently attracted considerable interest because they enable the simulation of complex biological systems on length-scales and timescales that are inaccessible for atomistic molecular dynamics simulation. A CG model is defined by a map that transforms an atomically detailed configuration into a CG configuration. For CG models of relatively small biomolecules or in cases that the CG and all-atom models have similar resolution, the construction of this map is relatively straightforward and can be guided by chemical intuition. However, it is more challenging to construct a CG map when large and complex domains of biomolecules have to be represented by relatively few CG sites. This work introduces a new and systematic methodology called essential dynamics coarse-graining (ED-CG). This approach constructs a CG map of the primary sequence at a chosen resolution for an arbitrarily complex biomolecule. In particular, the resulting ED-CG method variationally determines the CG sites that reflect the essential dynamics characterized by principal component analysis of an atomistic molecular dynamics trajectory. Numerical calculations illustrate this approach for the HIV-1 CA protein dimer and ATP-bound G-actin. Importantly, since the CG sites are constructed from the primary sequence of the biomolecule, the resulting ED-CG model may be better suited to appropriately explore protein conformational space than those from other CG methods at the same degree of resolution.