Guava (Psidium guajavaL.) is an important fruit crop of the Indian sub-continent, with potential for improvements in quality and yield. The goal of the present study was to construct a genetic linkage map in an intraspecific cross between the elite cultivar ‘Allahabad Safeda’ and the Purple Guava landrace to identify the genomic regions responsible for important fruit quality traits, viz., total soluble solids, titratable acidity, vitamin C, and sugars. This population was phenotyped in field trials (as a winter crop) for three consecutive years, and showed moderate-to-high values of heterogeneity coefficients along with higher heritability (60.0%–97.0%) and genetic-advance-over-mean values (13.23%–31.17%), suggesting minimal environmental influence on the expression of fruit-quality traits and indicating that these traits can be improved by phenotypic selection methods. Significant correlations and strong associations were also detected among fruit physico-chemical traits in segregating progeny. The constructed linkage map consisted of 195 markers distributed across 11 chromosomes, spanning a length of 1,604.47 cM (average inter-loci distance of 8.80 markers) and with 88.00% coverage of the guava genome. Fifty-eight quantitative trait loci (QTLs) were detected in three environments with best linear unbiased prediction (BLUP) values using the composite interval mapping algorithm of the BIP (biparental populations) module. The QTLs were distributed on seven different chromosomes, explaining 10.95%–17.77% of phenotypic variance, with the highest LOD score being 5.96 for qTSS.AS.pau-6.2. Thirteen QTLs detected across multiple environments with BLUPs indicate stability and utility in a future breeding program for guava. Furthermore, seven QTL clusters with stable or common individual QTLs affecting two or more different traits were located on six linkage groups (LGs), explaining the correlation among fruit-quality traits. Thus, the multiple environmental evaluations conducted here have increased our understanding of the molecular basis of phenotypic variation, providing the basis for future high-resolution fine-mapping and paving the way for marker-assisted breeding of fruit-quality traits.