Needle-based procedures are commonly performed during minimally invasive surgery for treatment and diagnosis. Accurate needle tip placement is important for the success of the procedures. Misplacement of the needle tip might cause unsuccessful treatment or misdiagnosis. Robot-assisted needle insertion systems have been developed in order to steer flexible bevel-tipped needles. However, current systems depend on the information of maximum needle curvature, which is estimated by performing prior insertions. This work presents a new three-dimensional flexible needle steering system which integrates an optimal steering control, ultrasound-based needle tracking system, needle deflection model, online needle curvature estimation and offline curvature estimation based on biomechanics properties. The online and the offline curvature estimations are used to update the steering control in real time. The system is evaluated by experiments in gelatin phantoms and biological tissues (chicken breast tissues). The average targeting error in gelatin phantoms is 0.42 ± 0.17 mm, and in biological tissues is 1.63 ± 0.29 mm. The system is able to accurately steer a flexible needle in multi-layer phantoms and biological tissues without performing prior insertions to estimate the maximum needle curvature.