Neutron powder diffraction and magnetization measurements of the Bi1-xCaxFeO3 (0.05 ≤ x ≤ 0.14) compounds were carried out to follow the effect of the heterovalent A-site doping on the long-range structure and magnetic properties of the BiFeO3 multiferroic. Ca substitution induces the appearance of weak ferromagnetism in the initial ferroelectric R3c phase, but modifies the picture of polar displacements, so the average PbZrO3-like antiferroelectric structure is stabilized at x = 0.11. Further increase of the Ca content leads to transformation of the antipolar ionic shifts to give rise to the Pbam → Imma transition near x = 0.14. A structural study performed for the x = 0.05 compound at high temperature revealed the R3c → Pnma phase transition at 950 K. For x = 0.1 samples, an intermediate heating-induced structure separating the R3c and Pnma phases was found.