In EUROCRYPT 2009, Galbraithh, Lin and Scott constructed efficiently computable endomorphisms for a large family of elliptic curves defined over finite fields of large characteristic. The scalar multiplication on GLS curves can be accelerated while the GLV method is applied. In this talk, we introduce our recent work on extending the method to the Jacobians of genus 2 hyperelliptic curves defined over binary fields. We give explicit formulae of endomorphisms on the Jacobians for the twisted curves of every isomorphism class of genus 2 hyperelliptic curves over binary fields. We investigate the benefits of fast scalar multiplication using various simultaneous scalar multiplication methods and show a speedup for up to 40% for a 256-bit scalar multiplication comparing with the best general ordinary methods.