Conjugate Gradient (CG) is one of the most popular iterative approaches in solving large sparse linear system of equations. This paper reports a parallel implementation of the Conjugate Gradient (CG) algorithm on clusters with EARTH multithreaded runtime support. In our implementation, the inter-phase and intra-phase communication costs are well balanced with a two-dimensional blocking method, minimizing the overall communication cost. EARTH architecture, with its adaptive, event-driven multithreaded execution model, gives additional opportunities to overlap communication and computation to achieve even better scalability. Experiments have been done on Chiba City, a 256 dual CPU cluster in Argonne National Laboratory (ANL). Notable improvements over other CG parallel implementations have been observed. For example, with the NAS CG benchmark problem size Class C, our implementation achieved relative speedup of 41 on a 64-node Chiba City cluster (with Ethernet connection), while the original NAS parallel CG implemented with MPI achieved only 13. Even though most clusters have relatively slow inter-node connection compared with the computing capability of their processors, the results demonstrate that the combination of the two-dimensional blocking method and the EARTH architectural runtime support helps to speed up the CG algorithm significantly on clusters by reducing and hiding the communication latency, making the clusters an even better platform for large scale parallel scientific computations.