Cervical cancer is one of the leading causes of cancer death among females worldwide and its behavior epidemiologically likes a venereal disease of low infectiousness. Early age at first intercourse and multiple sexual partners have been shown to exert strong effects on risk. Genital Human papilloma virus is the central risk factor for developing cervical cancer. Ethiopia has a population of 36.9 million women ages 15 years and older who are at risk of developing cervical cancer. Its incidence is 31.0 per 100,000 women with 7,445 annual number of new cases and 5,338 deaths every year. In order to investigate the epidemiology of cervical cancer associated with the human papillomavirus in Ethiopia, I construct mathematical model for progression of human papilloma virus with vaccination intervention; and I took into consideration nonlinear ordinary differential equations. I used a nonlinear stability analysis method for proving the local and global stability of the existing equilibrium point. I proved that the disease free equilibrium point is locally asymptotically stable and also globally asymptotically stable. Using second generation matrix, I obtained the effective and basic reproduction number for the dynamical system.Using standard parameter estimation I found that the numerical value of effective reproduction number is  and the basic reproduction number is . From this numerical value it is possible to conclude that vaccination intervention strategy is effective to control the spread of human papilloma virus diseases. The most sensitive parameter is  the proportion rate of vaccinated Individuals. I also conduct numerical simulations which support the finding in the sensitivity analysis.