The modular multilevel dc-dc converter(MMDC) has attracted much interest in medium voltage dc applications, but it has to face the main issue of balancing submodule(SM) capacitor voltages. This paper proposes a dual-circulant modulation and mathematically proves it possessing the inherent balancing capability for arbitrary operation cases. Two sets of circular switching patterns are preset and combined to complete the full constrains on SM voltages for balancing, and then reallocated to keep the advantage of SM uniformity. The associated polynomial of circulant matrix is introduced and the coprime of polynomials demonstrates the full-rank feature of the extended switching matrix that promises the inherent balancing. Experiments are conducted on prototype to validate the inherent voltage balancing capability of the dual-circulant modulation.