  We propose the superintegrable generalization of Smorodinsky-Winternitz
system on the $N$-dimensional complex Euclidian space which is specified by the
presence of constant magnetic field. We find out that in addition to $2N$
Liouville integrals the system has additional functionally independent
constants of motion, and compute their symmetry algebra. We perform the
Kustaanheimo-Stiefel transformation of $\mathbb{C}^2$- Smorodinsky-Winternitz
system to the (three-dimensional) generalized MICZ-Kepler problem and find the
symmetry algebra of the latter one. We observe that constant magnetic field
appearing in the initial system has no qualitative impact on the resulting
system.
