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The 3-RRR+(S-P) spherical parallel mechanism is very similar to human shoulder and hip joint. This mechanism can be taken as the prototype of the shoulder and hip joint for humanoid robot. However, the secure workspace of 3-RRR+(S-P) spherical parallel mechanism is so small, that could not meet the requirements of the shoulder and hip joint for humanoid robot. According to bionics and structure of human thighbone, the design idea of biasing output was proposed. And then, the 3-RRR+(S-P) bionic joint mechanism with biasing output was proposed based on the 3-RRR+(S-P) spherical parallel mechanism. For the bionic joint mechanism and prototype mechanism, there was a certain mapping relation between their secure workspaces. The mapping relation was obtained based on conversion of coordinates, and then, the secure workspace of the proposed bionic joint mechanism was obtained. The 3-RRR+(S-P) bionic joint mechanism with biasing output retained the kinematic and mechanical performance of prototype mechanism, and had a substantially increased secure workspace. The secure workspace of the proposed bionic joint mechanism could meet the requirements of the shoulder and hip joint for humanoid robot absolutely.