Model predictive control (MPC), originally developed in the community of industrial process control, is a potentially effective approach to optimal scheduling of cancer therapy. The basis of MPC is usually a state-space model (a system of ordinary differential equations), whereby existing studies usually assume that the entire states can be directly measured. This paper aims to demonstrate that when the system states are not fully measurable, in conjunction with model parameter discrepancy, MPC is still a useful method for cancer treatment. This aim is achieved through the application of moving horizon estimation (MHE), an optimisation-based method to jointly estimate the system states and parameters. The effectiveness of the MPC-MHE scheme is illustrated through scheduling the dose of tamoxifen for simulated tumour-bearing patients, and the impact of estimation horizon and magnitude of parameter discrepancy is also investigated.