NGC 188 is a good laboratory for studying the formation and evolution of W UMa type contact binaries due to its rich populations of them. We present a detailed photometric study of three short-period close binaries, EP Cep, ES Cep, and V369 Cep, in the old open cluster NGC 188 based on our two-set photometric observations. We discovered that both EP Cep and ES Cep are shallow-contact binaries with continuously decreasing periods. The difference is in their mass ratios. EP Cep has an extremely low-mass ratio, q=0.15, while ES Cep has a relatively high-mass ratio, q=0.69, indicating that they lie in different evolutionary stages. ES Cep is likely a newly formed contact binary via a Case A mass transfer, while EP Cep is an evolved system and may be on the oscillations caused by the combined effect of the thermal relaxation oscillation and the variable angular momentum loss. For another system, V369 Cep, we found that it is a primary-filling near-contact binary. Both the semidetached configuration and the continuous decrease in the orbital period indicate that it is undergoing a mass transfer from the primary component to the secondary one. This conclusion is in agreement with the excess luminosity seen in the light curves on the ingress of the secondary minimum produced by the impact of the mass transfer. All of the results suggest that V369 Cep is evolving into contact, and a shallow-contact high-mass ratio system similar to ES Cep will be formed. Then, it will evolve into a low-mass ratio contact binary just like EP Cep, and finally merge into a rapidly rotating single star.