The article deals with the effect of the conditions of modification of a natural aluminosilicate catalyst with a 10% HCl solution on the chemical and phase compositions, porous and crystal structures, and acidity of the material and on its catalytic properties in α-pinene isomerization. Treatment of the aluminosilicate with 10% HCl (25–250 mL per gram of solid) causes cation exchange, increases the concentration of protonic sites on the aluminosilicate surface, and removes impurity calcite and dolomite. The specific surface area of the aluminosilicate increases from 52 to 68–82 m2/g. Treatment of the aluminosilicate with 175.0 or 250.0 mL/g of HCl removes a considerable amount framework Al3+, Fe2+/3+, and Mg2+ cations, leading to a partial disruption of its structure and to a decrease in its acidity, specific surface area, and, as a consequence, catalytic activity relative to the same parameters of the samples treated with 50 or 100 mL/g of HCl. The highest catalytic activity is displayed by the aluminosilicate treated with 50 mL/g of HCl. The camphene and dipentene selectivity of the reaction (at 85% α-pinene conversion) with the original catalyst is 55 and 30%, respectively; modifying the aluminosilicate with HCl raises the camphene selectivity and reduces the dipentene selectivity by 5–6%. The catalyst considered here is more active than the commercial titanium catalyst.