  We present the first example of super Landau model with both N=4 worldline
supersymmetry and non-trivial target space supersymmetry ISU(2|2). The model
also reveals a hidden second N=4 supersymmetry which, together with the
manifest one, close on a worldline SU(2|2). We start from an off-shell action
in bi-harmonic N=4, d=1 superspace and come to the component action with four
bosonic and four fermionic fields. Its bosonic core is the action of
generalized U(1) Landau model on R^4 considered some time ago by Elvang and
Polchinski. At each Landau level N>0 the wave functions are shown to form
"atypical" (2N + 2N)-dimensional multiplets of the worldline supergroup
SU(2|2). Some states have negative norms, but this trouble can be evaded by
redefining the inner product, like in other super Landau models. We promote the
action to the most general form compatible with off-shell N=4 worldline
supersymmetry and find the corresponding background U(1) gauge field to be
generic self-dual on R^4 and the target superspace metric to remain flat.
