${\displaystyle x=\cos u+v\cos {\frac {u}{2}}\cos u}$

${\displaystyle y=\sin u+v\cos {\frac {u}{2}}\sin u}$

${\displaystyle z=v\sin {\frac {u}{2}}}$

MoebiusStrip[r_:1] =
  Function[{u, v}, 
    r {Cos[u] + v Cos[u/2]Cos[u], Sin[u] + v Cos[u/2]Sin[u], v Sin[u/2]}
  ]

ParametricPlot3D[Evaluate[MoebiusStrip[][u, v]], {u, 0, 4π}, {v, 0, .3},