Solution to a generalized interval eigenvalues equation is studied by denoting the interval parameters of uncertain structure with universal grey numbers, and a concise algorithm is presented. It is showed that universal grey mathematics can deal with some problems that interval analysis can′t by analysing interval problem with extensible characteristic of universal grey number. Then the solution to the interval eigenvalues equation is achieved with universal grey mathematics method, which is based on the characteristic of Rayleigh quotient and the monotonicity of interval eigenvalues. Finally, two examples are employed to show that this method is simple, accurate and reliable.