In the field of radiotherapy, Monte Carlo (MC) particle transport calculations are recognized for their superior accuracy in predicting dose and fluence distributions in patient geometries compared to analytical algorithms which are generally used for treatment planning due to their shorter execution times. In this work, a newly developed MC-based treatment planning (MCTP) tool for proton therapy is proposed to support treatment planning studies and research applications. It allows for single-field and simultaneous multiple-field optimization in realistic treatment scenarios and is based on the MC code FLUKA. Relative biological effectiveness (RBE)-weighted dose is optimized either with the common approach using a constant RBE of 1.1 or using a variable RBE according to radiobiological input tables. A validated reimplementation of the local effect model was used in this work to generate radiobiological input tables. Examples of treatment plans in water phantoms and in patient-CT geometries together with an experimental dosimetric validation of the plans are presented for clinical treatment parameters as used at the Italian National Center for Oncological Hadron Therapy. To conclude, a versatile MCTP tool for proton therapy was developed and validated for realistic patient treatment scenarios against dosimetric measurements and commercial analytical TP calculations. It is aimed to be used in future for research and to support treatment planning at state-of-the-art ion beam therapy facilities.