Multi-element trace analysis by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) of high-purity metals, semiconductors and insulators (e.g., ceramics) is often limited by the lack of suitable standard reference materials (SRM) with the same matrix composition and also a lack of a significant number of certified trace element concentrations in the available SRMs. This paper describes a new and easy standard-free quantification strategy using solution-based calibration for the multi-element determination of trace impurities in high-purity platinum. For the mass spectrometric measurements, a quadrupole-based LA-ICP-MS instrument was coupled with an ultrasonic nebulizer (USN). Due to the lack of a high-purity blank platinum sample, quantification of the results of LA-ICP-MS measurements was carried out using the standard additions mode in solution-based calibration. In order to achieve matrix matching, the multi-element standard solutions (with different concentrations of analytes) were nebulized successively with a USN. Simultaneously the high-purity platinum target was ablated with a focused laser beam during solution calibration with the USN. The mass spectrometric method developed was validated using a platinum standard reference material (NIST SRM 681). The analytical results of the LA-ICP-MS of SRM 681 Platinum are in good agreement with the certified values. The relative standard deviation (RSD) of most elements (n = 3) is between 2 and 10%. The proposed analysis method can be applied for other high-purity materials in a similar way, e.g., for trace and ultratrace analysis of high-purity metals, semiconductors and insulators such as high-purity ceramics.