This　paper　develops　an　incremental　randomized　learning　method　for　an　extended　Echo　State　Network　(phi-ESN),　which　has　a　reservoir　with　random　static　projection,　to　better　cope　with　non-linear　time　series　data　modelling　problems.　Although　the　typical　ESN　can　effectively　improve　the　prediction　performance　of　the　network　by　extending　a　random　static　nonlinear　hidden　layer,　since　the　input　weights　and　biases　of　the　hidden　neurons　in　the　extended　static　layer　are　randomly　assigned,　some　neurons　have　little　effect　on　reducing　the　model　error,　resulting　in　high　model　complexity,　poor　generalization　and　large　performance　fluctuation.　A　constructive　incremental　randomized　learning　method　termed　OLS-phi-ESN　is　proposed　for　generating　the　nodes　of　the　extended　static　nonlinear　hidden　layer.　Two-step　training　paradigm　is　adopted,　namely,　randomly　assigning　the　input　weights　and　biases　of　the　hidden　neurons　in　the　extended　static　layer　according　to　a　supervisory　mechanism　and　solving　output　weights　by　least　squares　algorithm.　Based　on　Orthogonal　Least　Squares　(OLS)　search　algorithm,　the　proposed　supervisory　mechanism　is　designed　where　an　adaptive　threshold　is　also　set　to　better　control　the　compactness　of　the　generated　learner　model.　Simulation　results　concerning　both　nonlinear　time　series　prediction　and　system　identification　tasks　indicate　some　advantages　of　our　proposed　OLS-phi-ESN　in　terms　of　more　compact　model　and　sound　generalization.