Our aim is to demonstrate the feasibility of fast Monte Carlo (MC)-based inverse biological planning for the treatment of head and neck tumors in spot-scanning proton therapy. Recently, a fast and accurate graphics processor unit (GPU)-based MC simulation of proton transport was developed and used as the dose-calculation engine in a GPU-accelerated intensity modulated proton therapy (IMPT) optimizer. Besides dose, the MC can simultaneously score the dose-averaged linear energy transfer (LETd), which makes biological dose (BD) optimization possible. To convert from LETd to BD, a simple linear relation was assumed. By use of this novel optimizer, inverse biological planning was applied to 4 patients, including 2 small and 1 large thyroid tumor targets, as well as 1 glioma case. To create these plans, constraints were placed to maintain the physical dose (PD) within 1.25 times the prescription while maximizing target BD. For comparison, conventional intensity modulated radiation therapy (IMRT) and IMPT plans were also created using Eclipse (Varian Medical Systems) in each case.The same critical-structure PD constraints were used for the IMRT, IMPT, and biologically optimized plans. The BD distributions for the IMPT plans were obtained through MC recalculations. Compared with standard IMPT, the biologically optimal plans for patients with small tumor targets displayed a BD escalation that was around twice the PD increase. Dose sparing to critical structures was improved compared with both IMRT and IMPT. No significant BD increase could be achieved for the large thyroid tumor case and when the presence of critical structures mitigated the contribution of additional fields.The calculation of the biologically optimized plans can be completed in a clinically viable time (<30minutes) on a small 24-GPU system. By exploiting GPU acceleration, MC-based, biologically optimized plans were created for small-tumor target patients. This optimizer will be used inan upcoming feasibility trial on LETd painting for radioresistant tumors.