This　paper　focuses　on　a　method　to　construct　wavelet　Riesz　bases　with　homogeneous　boundary　condition　and　use　them　to　a　kind　of　second-order　elliptic　equation.　First,　we　construct　the　splines　on　the　interval　[0,1]　and　consider　their　approximation　properties.　Then　we　define　the　wavelet　bases　and　illustrate　the　condition　numbers　of　stiffness　matrices　are　small　and　bounded.　Finally,　several　numerical　examples　show　that　our　approach　performs　efficiently.