We study the binding energy of excitons in a cylindrical GaAs/Ga1−xAlxAs nanowire superlattice, embedded in Ga1−yAlyAs matrix, in the presence of magnetic and electric fields applied parallel to the growth direction. We express the exciton trial function as a product of one-particle wave functions of the electron and the hole with variationally determined envelope function, which describes the exciton intrinsic properties and depends only on the electron-hole separation. By using a functional derivative technique, we derive a differential equation for this envelope function, which we solve numerically. By varying the wire radius, interwell barrier width and well sizes we obtain binding energies ranging in character from one for strongly coupled superlattice to that for a system of stack of isolated disks. The behaviour of the binding energies and the charge distributions as functions of the interwell coupling, well sizes, and the external fields is consistently described with our simple formalism.