Linear and nonlinear viscoelastic properties of an asymmetric triblock copolymer poly(acrylic acid)-poly(2-vinylpyridine)-poly(acrylic acid) (PAA-P2VP-PAA) in salt-free aqueous solutions have been investigated. At pH 3.4, long-range electrostatic interactions prevail, due to protonated P2VP units and negative PAA end groups. Above a critical C-g = 2.5% w/w, a transient network is formed through intermolecular electrostatic interactions between negatively charged groups located at the end PAA blocks and positively charged protonated pyridine groups located at the middle long P2VP block. The so-formed network exhibits some atypical rheological behavior characterized by a strain hardening of storage modulus in intermediate strain amplitudes and a pronounced shear thickening in moderated shear stresses. The shear-induced changes in the structure of the network have been attributed to enhancement of the number of elastically active bridges through association of free dangling ends and a transition from intra- to intermolecular association.