Nonreciprocal unidirectional absorption, as a critical feature in both applications of military and civilian, has always been a challenging research topic. Here, we introduce a linear incremental arrangement into the formation of the electromagnetically induced absorption (EIA) in a single metastructure unit, creating an asymmetry spatial modulation for the nonreciprocal electromagnetic responses. A unidirectional EIA peak with a high absorption reaching 87.87% is observed for the forward case, and nearly all the incident energy is reflected in the backward case. The maximum isolation ratio (IR) between the forward and backward absorptions is 10.79 dB. To obtain a higher forward absorption and enlarge the IR, an improved nonreciprocal metastructure array is proposed and experimentally demonstrated by applying a linear quasi-periodic array configuration. The forward electromagnetically induced unidirectional absorption is enhanced to 99.53% with an IR of 12.73 dB. The near-perfect absorption provides a promising platform for permittivity sensing, and the measurement of common microwave plates with different relative permittivity shows an excellent linear regression. Such an implementation innovatively combines the asymmetric spatial modulation with EIA to form unidirectional absorption, offering a new guideline for novel nonreciprocal devices, and possessing considerable practical applications in the wireless communication system, ultrasensitive sensing, one-way invisibility, and absorptive switching.