A During last two decades, there has been a prolific growth in the chaos based image encryption algorithms. Up to an extent these algorithms have been able to provide an alternative to exchange large media files (images and videos) over the networks in a secure way. However, there have been some issues with the implementation of chaos based image ciphers in practice. One of them is reduced/small key space due to the fact that chaotic behavior is only observed for certain range of system parameters/initial conditions of the chaotic system used in such algorithms. To overcome this difficulty, we propose a simple, efficient and robust image encryption algorithm based on combined applications of quasigroups and chaotic standard map. The proposed image cipher is based on the popular substitution-diffusion architecture (Shanon) where a quasigroup of order 256 and chaotic standard map have been used for the substitution and permutation of image pixels respectively. Due to the introduction of quasigroup as part of the secret key along with the parameter and initial conditions of the chaotic standard map, the key space has been increased significantly. The proposed image cipher is very fast due to the fact that the substitution based on the quasigroup operations is very simple and can be executed easily through the lookup table operations on Latin squares (which are Cayley operation tables of quasigroups) and the permutation is performed row-by-row as well as column-by-column using the pseudo random number sequences gener-ated through the chaotic standard map. The security and performance have been analyzed through the histograms, correlation coefficients, information entropy, key sensitivity analysis, differential analysis, key space analysis etc. and the results prove the efficiency and robustness of the proposed image cipher against the possible security threats.