Linear time mu-calculus (μTL) is an extension of linear-time temporal logic (LTL) by fixed points, which is a convenient way to specify and reasoning about reactive systems. As μTL being more expressible than LTL, the properties specified by LTL could be determined by μTL. Similar to the intuitionistic linear-time temporal logic (ILTL), we propose an intuitionistic variant of μTL as intuitionistic linear time mu-calculus (IμTL). We have established a correspondence between ImTL and ILTL, and compared their expressive power. Using IμTL to specify safety and liveness properties, and assumption-guarantee specifications are also discussed.