Photoacoustic　imaging　(PAI)　is　a　fast-developing　biomedical　imaging　technology　suitable　for　noninvasive　structural　and　functional　imaging.　Image　reconstruction　of　PAI　requires　the　solution　of　an　inverse　source　problem,　where　the　source　represents　the　optical　energy　absorption　distribution　in　the　object.　PAI　in　spherical　or　circular　geometry　gives　good　image　resolution　yet　is　slow　in　signal　acquisition　and　image　formation.　Reducing　the　number　of　detection　angles　can　ameliorate　such　issues.　Besides,　it　is　almost　impossible　to　cover　the　entire　surface　of　tissue.　This　will　restrict　it　in　the　medical　application　with　incomplete　projection　data.　To　resolve　such　limiting　factors,　in　this　thesis,　a　preconditioned　conjugate　gradient　method　is　applied　to　the　normal　equations　(PCCGNR　method)　for　reconstructing　the　absorption　distribution.　Under　the　common　assumption,　a　zero-mean　Gaussian　noise　is　added　to　the　projection　signals　and　a　computer　simulated　has　been　used　for　the　evaluation.　This　algorithm　works　well　in　rectification　of　the　measurement　and　converges　quickly　onto　an　accurate　estimate　of　the　distribution　of　absolute　absorption.　It　not　only　runs　much　faster　than　the　FBP　algorithm,　but　also　shows　stronger　robustness　in　that　it　provides　better　image　quality　with　detection　data.　We　observed　that　diagonal　preconditioners　offer　some　improvement　in　convergence　rate　for　image　reconstruction,　and　reconstructed　image　preconditioning　with　omega　=　0　(diagonal　scaling)　is　closer　to　the　true　image　than　with　omega　＞　0.　In　addition,　a　physical　experiment　that　will　be　done　with　our　experiment　equipment　system　further　demonstrates　the　potential　of　the　proposed　algorithm　in　practical　applications.