A passive magnetic field cancellation device (PMFCD) is designed. The PMFCD could automatically cancel the field as an active cancellation system did; however it requires no power sources and feedback systems. The capability of the PMFCD is based on the principle that a closed loop can resist flux variation and keep the flux constant inside. The closed loop in the PMFCD is formed by connecting two pairs of high temperature superconductor Helmholtz coils with different radii in series. More important thing is that the ratio of the radius and the turn number between the coils has to satisfy a number of conditions, with which 100% cancellation can be reached. Theoretical methods to obtain the turn number ratio and radius ratio are the major part of the paper. Numerical simulation was followed, aiming to evaluate field distribution under a cancellation state and correct the theoretical values.