The 'molecular' value of the nuclear quadrupole moment of the As-75 nucleus is determined combining the experimental data for quadrupole coupling constant and the calculated electric field gradient in the AsP molecule. The accurate calculations have been carried out at the CCSD(T) level. The relativistic effects were accounted for using the infinite-order two-component method in the scalar approximation. The new recommended value of the nuclear quadrupole moment of 75As obtained in this work is 311( 2) mb and is more precise than the previous 'muonic' value. (C) 2010 Elsevier B.V. All rights reserved.