This paper describes the higher-order moment analysis of superposed Markov jumping processes. A superposed Markov jumping process is defined as a linear superposition of a finite number of piecewise constant real valued stochastic process whose value changes are associated with state transitions in an underlying descrete state continuous time Markov process. Some phenomena are modeled well by the process such as membrane current fluctuations observed at bio-membranes or load fluctuations in electrical power systems. Theoretical formula of the moment function of any order k is derived and the parameter estimation problem utilizing higher-order moment functions is discussed. A new method of estimating the kinetic parameters of membrane current fluctuations is proposed as a possible application.