We propose an estimation method using a recurrent neural network (RNN) of the colon's shape where deformation was occurred by a colonoscope insertion. Colonoscope tracking or a navigation system that navigates physician to polyp positions is needed to reduce such complications as colon perforation. Previous tracking methods caused large tracking errors at the transverse and sigmoid colons because these areas largely deform during colonoscope insertion. Colon deformation should be taken into account in tracking processes. We propose a colon deformation estimation method using RNN and obtain the colonoscope shape from electromagnetic sensors during its insertion into the colon. This method obtains positional, directional, and an insertion length from the colonoscope shape. From its shape, we also calculate the relative features that represent the positional and directional relationships between two points on a colonoscope. Long short-term memory is used to estimate the current colon shape from the past transition of the features of the colonoscope shape. We performed colon shape estimation in a phantom study and correctly estimated the colon shapes during colonoscope insertion with 12.39 (mm) estimation error.