The purposes of this research study were to develop solving-problems in science learning approach with the Problem-Based Learning (PBL) instructional lesson plans to enhance students’ learning achievements and their solving-problem abilities in science with the efficiency of the processing performances and the performance results (E1/E2) at the determining criteria as 80/80, students’ learning achievements of their post assessing test and the criteria learning outcomes at 80% with the PBL, and students’ solving-problem abilities and the criteria learning outcomes at 80% with the PBL toward science were compared, and to associate between students’ learning achievements and their solving-problem abilities with the PBL was analyzed. Administrations with a sample size which consisted of 48 lower secondary educational students at the 9th grade level from Wapi Phatum School under the Maha Sarakham Secondary Educational Service Area Office 26 with the purposive sampling random technique was selected. Using the 6-main instructional PBL method’s lesson plans to management of the activity-based learning conceptual approach in 12 hours, the 30-item Learning Achievement Assessing Test (LAAT), and the 20-item Solving-Problem Ability Measuring Test (SPAMT) were used. Statistically significant with the average mean scores, standard deviation, percentage, independent variable t-test were analyzed, simple and multiple correlations, standardized regression weight validity, and coefficient predictive value (R2) were associated. The results of these research findings have revealed as: students were evaluated to determine performance criteria with the efficiency of the E1/E2 results with the PBL method indicated that of 85.48/84.44, which was higher than standardized criteria of 80/80. Students’ learning achievements of their post assessing test and the scientific solving-problem learning ability outcomes at 80% with the PBL were differentiated that evidence at the 0.05 level, significantly. Students’ performances of their SPAMT and the criteria learning outcomes at 80% with the PBL toward science were also found of statistically significant that evidence of 0.01, differently. Associations between students’ learning outcomes of their LAAT and their SPAMT toward science, the R2 value indicates that 67% of the variance in solving-problem abilities to their science class was attributable to their learning achievements of their Problem-Based Learning (PBL) instructional method toward science.