For the evaluation of pathological gait, a machine learning-based estimation of the vertical ground reaction force (vGRF) using a low-cost insole is proposed as an alternative to costly force plates. However, learning a model for estimation still relies on the use of force plates, which is not accessible in small clinics and individuals. Therefore, this paper presents a force plate-free learning from a single leg stance (SLS) and natural walking measured only by the insoles. This method used a linear least squares regression that fits insole measurements during SLS to body weight in order to learn a model to estimate vGRF during walking. Constraints were added to the regression so that vGRF estimates during walking were of proper magnitude, and the constraint bounds were newly defined as a linear function of stance duration. Moreover, a lower bound for the estimated vGRF in mid-stance was added to the constraints to enhance estimation accuracy. The vGRF estimated by the proposed method was compared with force platforms for 4 healthy young adults and 13 elderly adults including patients with mild osteoarthritis, knee pain, and valgus hallux. Through the experiments, the proposed learning method had a normalized root mean squared error under 10% for healthy young and elderly adults with stance durations within a certain range (600-800 ms). From these results, the validity of the proposed learning method was verified for various users requiring assessment in the field of medicine and healthcare.