We studied GMI effect and magnetic properties of Finemet-type FeCuNbSiB microwires. We observed that GMI magnetic field and frequency dependences and magnetic softness of composite microwires produced by the Taylor-Ulitovski technique can be tailored either controlling magnetoelastic anisotropy of as-prepared FeCuNbSiB microwires or controlling their structure by heat treatment or changing the fabrication conditions. GMI effect has been observed in as-prepared Fe-rich microwires with nanocrystalline structure.This work was supported by EU ERA-NET programme under project "SoMaMicSens" (MANUN ET-2010-Basque-3), by EU under FP7 "EM-safety" project, by Spanish Ministry of Science and Innovation, MICINN under Project MAT2010-18914, by the Basque Government under Saiotek 11 MICMAGN project (S-PE11UN087) and by federal target program "Scientific and scientific-pedagogical personnel of innovative Russia", state contract No. 14.18.21.0783