It is well-known that a nullor of the negative-type is a two-port with the null transmission matrix. But there is no obviously mathematical definition for a plus-type nullor. The authors proposed a matrix definition for a nullor of the plus-type. Besides, this paper derived the adjoint network for a plus-type nullor to obtain the conversions between voltage-mode circuits and current-mode circuits which are originally with plus-type nullors. Examples for the voltage-mode amplifier, the filter and the oscillator with plus-type nullor were given, their current-mode counterparts are derived by applying the adjoint transformation. Simulated and experimental results are given to confirm with the theoretical analysis.